It was the 22-time grand slam winner who convinced husband Andre Agassi to try and steer Novak Djokovic back into top form.
"It was a surprise for me," Agassi tells Pat Cash for CNN's Open Court of his appointment, which Djokovic had been mulling over for weeks.
Since retiring in 2006, the Las Vegas native has been heavily involved in several charities, while mostly staying out of the limelight.
"I did say no a couple of times," Agassi admits, while explaining Graf's perseverance. "She said 'Gosh, I hear you talking to (Djokovic), and I hear you talking about him. Why don't you go spend a little time and get to know him?'
"So, either she wants me out of the house, or she really cares and knows me."
In an unusual move, Agassi says that he is not accepting payment for his coaching role.
"I'm interested in helping him on terms that work for both of us," he explains. "I'm not doing this (to get paid) nor do I want to get paid. That's not what I'm interested in.
"I'm inspired because of inspiration itself. I'm at a very blessed time in my life and I don't really need anything. It's not something I'm worried about."
Although Agassi is unable to remain in Paris for the tournament's duration because of a prior commitment, he watched attentively from the player's box as Djokovic advanced during the first week.
The current world No. 2 meets Dominic Thiem of Austria in the quarterfinals Tuesday.
A loss of form
Only a year ago coaching Djokovic appeared to be one of sports' cushiest jobs.
The Serbian had just won the French Open, completing the first calendar grand slam in men's singles tennis in 47 years,
and was playing with an air of invincibility.
But not much has gone right since.
In his Wimbledon title defence, Djokovic suffered a third-round defeat to unseeded American Sam Querrey, and was knocked out of the 2016 Olympics in the first round by a resurgent Juan Martín del Potro.
By the end of the year, Djokovic had lost his world No. 1 ranking to Andy Murray, ushering a parting of ways with his mentor of three seasons Boris Becker.
This year began with an embarrassing second-round exit at the 2017 Australian Open at the hands of then-world no. 117 Denis Istomin. In May, the 30-year-old dropped longtime coach Marian Vajda along with his trainer and physiotherapist.
What Agassi -- an eight-time grand slam winner, and the oldest man ever to hold the world No. 1 ranking at age 33 -- can offer as Djokovic's new coach remains to be seen.
"Understanding him has been my top priority; understanding his processes and how he sees his own game," Agassi says.
"One of the first thing I asked him is, 'What do you think makes you so good?'"
The 47-year-old Agassi has never coached on a professional level, and his appointment was announced only eight days before the start of the French Open.
"We are both excited to work together and see where it takes us," Djokovic said after his partnership with Agassi was announced. "It's just us trying to get to know each other in Paris a little bit.
"Obviously, Andre is someone that I have tremendous respect for as a person and as a player. He has been through everything that I'm going through."
Agassi will be able to relate to the change of lifestyle that faces Djokovic, who is expecting a second child with wife Jelena.
Both of Agassi's children were born during his playing career, and Becker has hinted that Djokovic's family life was beginning to take precedence over training.
"The last six months have been challenging on many levels," Becker told Sky TV shortly after the pair split in December. "Naturally he wanted to spend more time with his family. He wanted to pursue other off-court interests, rightfully.
"As a coaching staff our hands were tied a little bit. We couldn't do the work we wanted to do, because he had more important things to do. So then we questioned ourselves: Why are we going to New York (for the US Open)?
"Once you raise that question, that is the beginning (of the end)."
Part of a top player's responsibility, says Agassi, is constantly tweaking training habits to match personal situations.
"There is not a lot of margin out there when you're living on a razor's edge against the best in the world," he says. "You gotta have that right balance. I certainly understand what I would do if I was him."
Highly tuned Ferrari
Because of Agassi's career arc -- which includes erratic play and tantrums as a young tennis bad boy, a surprising Wimbledon title at the age of 22, a bout of depression and drugs
, and finally a redemptive comeback featuring five majors -- he had recently been touted as a potential psychologist and motivator for the likes of Nick Kyrgios.
Though Agassi showed compassion for Kyrgios after his early exit in Australia in January, the American cited a lack of time and family commitment to taking a coaching role. (It is unlikely that the young Aussie reached out to Agassi, however.)
But the intrigue of coaching Djokovic, a former world No. 1 and health nut who is still in the prime of his career, was too good an opportunity to pass up.
"He's set a pretty high bar," says Agassi of his new pupil. "It's fair to say that might be the very challenge for me, that everyone sees (Djokovic) as only having down to go.
"It's easy to say that this person is like a highly tuned Ferrari, like what (more) can you do to it? But it's not quite that simple.
"You got a human mind and a human heart, and you certainly got ridiculous talent. But they do have to come together, and sometimes you need different ways to get to the same (results)."
"I know what he's done; it's obvious to everybody what he's capable of, but he's got to find new ways to do it," he adds.
"Redemption is not a horrible thing"
Meanwhile, Agassi says that two-time French Open winner Maria Sharapova should have been given a wild card entry at Roland Garros based on her contributions to the sport.
Sharapova returned to the tour in April after successfully appealing a two-year suspension for taking the previously-allowed drug meldonium in January 2016. Because of her absence on tour, the former world No. 1 has seen her ranking drop to 178.
"Would I have given it to her? Yeah I probably would have," Agassi says of the invitation to bypass the qualifying tournament to the French Open's main draw, which Sharapova's ranking did not entitle her to enter at the time of her return.
"She's meant a lot to this game. Whatever thing she was taking was legal her entire career (until its ban shortly before her failed drug test), and she's paid her dues with that. Redemption is not a horrible thing. More governance is always a good thing."
Sharapova is set to become the first former Wimbledon champion to play the tournament's qualifying campaign
, scheduled for the last week of June in the London suburb of Roehampton.