Swiss Attorney General Michael Lauber told journalists Wednesday in the Swiss city of Bern that he did not exclude interviewing Blatter and Secretary-General Jerome Valcke as the investigation deepens.
Swiss authorities had previously said that Blatter, who has announced he will step down as president, was not part of the inquiry.
Lauber also warned that it was going to be a lengthy investigation and that Swiss law prevented him from revealing any detail about it despite what he acknowledged was "enormous public interest" in the case.
"The world of football needs to be patient. By its nature, this investigation will take more than the legendary 90 minutes," he said, referring to the length of a soccer match.
Lauber added that so far, "the investigation is of great complexity and quite substantial. To give you an example, the Swiss Office of the Attorney General has seized around nine terabytes of data."
FIFA has been embroiled in scandal since the United States indicted 14 people, including nine top FIFA officials, on corruption charges last month.
The Swiss probe is running simultaneously with the U.S. investigation, but they are being conducted independently of each other, Lauber said. Data gleaned by his investigators will not automatically be shared with the U.S. side.
In an interview with CNN, Lauber said the Swiss investigation had "a different target" than its U.S. counterpart and was at an earlier stage in the process.
The Swiss probe was opened in March "against persons unknown on the grounds of suspicion of criminal mismanagement and of money laundering," he said earlier.
The Swiss investigation was launched on the basis of evidence from a report compiled by former U.S. Attorney Michael Garcia for FIFA and information from the U.S. Department of Justice as well as suspicious banking activities, Lauber told reporters.
Besides 104 "banking relations" already known to authorities, he said, each of which represents several bank accounts, banks had flagged up another 53 suspicious transactions via a Swiss anti-money laundering framework.
However, Lauber declined to put any value on the sums of money involved, saying some suspicious activities could involve the blocking of funds as well as transfers.
The secrecy surrounding the investigation is in part to prevent the loss of evidence, he said, either through records going missing or people talking to each other before they are formally interviewed.
So far, Swiss investigators have sought to interview 10 people, Lauber told CNN, but declined to say whether any of those were members of FIFA's executive committee. "It could go further. It is possible I could interview the FIFA president or secretary-general," he said.
FIFA has been cooperative, including in searches of its premises, he said, and passed Swiss authorities the Garcia file in the first place.
Blatter, as a Swiss national, cannot be extradited from Switzerland to any other country, he added.
Swiss attorney general 'very confident' in his team
Lauber said the complexity of the case was augmented by its global dimensions -- and the interest being paid from around the world. "It's one of the biggest cases I've ever seen," he said.
His investigators will have to follow links around the world, he said, and may encounter lawyers trying to slow the process down.
But Lauber said he is "very confident" that the team can follow the investigation through to a successful conclusion.
"No country in this world can really fight international phenomenons of money laundering or misconduct or corruption on its own. It needs partners abroad, and that's why I'm grateful to have good partners in the (U.S. Department of Justice)," he said.
In the United States, prosecutors have alleged that FIFA officials took more than $150 million in bribes to provide "lucrative media and marketing rights" to soccer tournaments.
Blatter is not one of those indicted. But U.S. officials told CNN earlier this month that the FBI corruption investigation into FIFA's president continues.
FIFA, which insists that any suspected wrongdoing concerns individuals rather than the organization as a whole, has said there are no legal grounds
for it to take the 2018 World Cup from Russia
or the 2022 event from Qatar.
However, Valcke announced last week that FIFA would "postpone" the bidding process for the 2026 World Cup as investigations continue into allegations that bribery helped determine the hosts of earlier events.