(CNN) -- Presidential hopeful Herman Cain told a newspaper Thursday that he never told his wife about another woman he befriended 13 years ago and helped out financially.
In an editorial board meeting with the New Hampshire Union Leader, Cain said he repeatedly gave Ginger White money to help her with "month-to-month bills and expenses." However, he denied a sexual affair, as White alleges.
Cain also said he was considering dropping out of the race, but for now was continuing to meet all campaign commitments. The statement in the videotaped interview was his most definitive to date that he might end his campaign.
Cain later told Sean Hannity of Fox News that he will make a decision before Monday.
On Wednesday night, Cain told reporters in Ohio that he had discussed White's allegations with his wife, but was waiting until he could speak face-to-face with Gloria Cain on Friday before making any decision about his campaign.
He said in the Thursday interview that his wife's feelings, as well as the reaction from supporters and donors, would be important factors in deciding whether to stay in the race.
"Yes, getting out is an option," Cain said in the interview, which lasted almost an hour.
The allegation of an extramarital affair, following accusations of sexual harassment from other women, has seriously damaged Cain's presidential bid. Once a surprise front-runner in the race, he has plunged in the polls since initial allegations of sexual harassment emerged in October.
Cain told staffers this week he was reassessing his campaign in the wake of White's allegation of an affair, and he acknowledged to reporters Wednesday that her account had led to a drop in campaign contributions.
On Thursday, Cain provided new details on his relationship with White, including the revelation that his wife had no knowledge of what he called a friendship dating back years and his financial help for the woman.
Gloria Cain "did not know that we were friends until she (White) came out with this story" on Monday, Cain said, later adding: "My wife did not know about it, and that was the revelation. My wife found out about it when she (White) went public with it."
Cain also repeated his insistence that he and White were no more than friends. He had previously denied any sexual relationship with White.
Asked about reports of text messages he had exchanged with White, Cain confirmed that the woman had sent him about 70 such messages between October 22 and November 18 including some "asking for financial assistance."
"She was out of work and had trouble paying her bills and I had known her as a friend," Cain said, adding: "She wasn't the only friend who I had helped in these tough economic times, and so her messages to me were relating to 'need money for rent' or whatever the case may be. I don't remember all the specifics."
Cain said he gave White money, but refused to divulge how much.
"My wife now knows," Cain said. "My wife and I have talked about it and I have explained it to her. My wife understands that I'm a soft-hearted, giving person."
Saying that no questions would have been raised if the story involved giving money to a needy male friend, Cain added that his wife "is comfortable with the explanation that I told her."
Cain's attorney, Lin Wood, told CNN's "Piers Morgan Tonight" on Thursday that White has provided no proof of an affair or associated financial receipts.
He claimed his client has been a victim of unproven allegations and that the media should be asking tough questions of White.
Referring to five women who have made allegations against Cain, Morgan asked Wood if it was stretching credulity to suggest that all "of these woman are simply fantasies."
"Let me suggest to you that five lies do not make one truth," Wood replied. "When you talk about the importance of character ... let's look at it from the perspective of that candidate's entire career and life. Don't judge people's character based on accusations made in the media that have not been proven with facts and, in fact, have been clearly denied by the candidate."
The attorney said it was improper to answer specifics about the friendship and financial arrangements between Cain and White.
"I am not going to relegate the political process into a Jerry Springer show," he said.
Cain told Hannity he is going to "re-establish" his character and get to the bottom of the circumstances of the allegations against him.
"I send checks to a lot of people. I help a lot of people," Cain said. "That in itself is not proof. So the other allegation in terms of it being a 13-year physical relationship, that is her words against my word."
Cain said Wednesday night that Friday will be the first opportunity to sit down with his wife and "walk through this" with his family.
On Thursday, an official with Cain's Iowa campaign staff said the candidate's chief of staff met with the four-person Iowa team to emphasize that the election drive was moving forward.
"Mark Block, Herman Cain's chief of staff and chief operating officer, just left a meeting at the Iowa headquarters with all four Iowa staffers," said a statement by Lisa Lockwood, the communications director of Friends of Herman Cain's Iowa staff. "The emphatic message is that the campaign is full steam ahead. Herman Cain is in it to win it. He always has been and that has not changed."
The Iowa caucuses, the first formal test of the primary season, are scheduled for January 3.
Two women -- Sharon Bialek and Karen Kraushaar -- have accused Cain of sexually harassing them in the 1990s while he was head of the National Restaurant Association. Two other women also have said Cain sexually harassed them while they worked at the association, but they have declined to be identified.
This week, White told the media that she had an off-and-on affair with Cain for about 13 years, which she described as "very casual."
In the interview Thursday, Cain speculated that political opponents might be paying White to make the allegations.
"Running for president is a very dirty game," he said, repeating: "It's a dirty game."
Cain also said he would drop out of the race if his wife asked him to, but quickly added that she wouldn't.
Gloria Cain rarely makes public appearances or statements. Earlier this month, she spoke to Fox News, calling the sexual-harassment allegations "unfounded."
In a fund-raising letter Tuesday night after White spoke to the media about the alleged relationship, Cain wrote that "a troubled Atlanta businesswoman used national media outlets to promulgate a fabricated, unsubstantiated story about a 13-year affair with me. I am writing you today to assure you that this woman's story is completely false."
On Wednesday morning White responded, "It's very disappointing that he would call me troubled."
"I'm only here to state the truth and what's happened in the past," she said on ABC's "Good Morning America."
She acknowledged that Cain has given her money. "I've received gifts and money for the last 2 1/2 years consistently," she said, adding that he did not ask for anything in return.
She and Cain were in touch until last week, when there were leaks about the relationship and members of the media began to call her cell phone and family members, White said.
White said she came forward to share her side of the story.
"I can't imagine waking up one morning and deciding to come out with this if this was not true," she told ABC. "This has been a very difficult situation for myself, for my family, and it's nothing that I am proud of."
"So far I have been absolutely humiliated, embarrassed," she said.
White said she had not saved receipts and notes throughout the affair because she never planned to make the relationship public.
But, she said, Cain took her on several trips, including to a boxing match in Las Vegas.
"I can't make this stuff up," she said.
Asked whether his recent texts to her included requests that she not come forward, she replied, "Absolutely not. The funny thing about Herman Cain is, never in a million years did he probably think that I would speak out on this. And honestly speaking, I never wanted to."
White acknowledged that she has been sued for libel by a former business partner. "There were disputes and disagreements" with the partner and the experience became emotional, she said, acknowledging that she had made mistakes. White said she thought the situation had been resolved.
Asked whether she believes Cain should end his campaign, White responded, "That's something he has to decide for himself."
CNN's Tom Cohen, Alan Silverleib, Josh Levs, Ashley Killough, Kevin Bohn, Gloria Borger, Peter Hamby, Wolf Blitzer and John King contributed to this report.