The paper quoted an unnamed source close to Blatter as saying he "had received messages of support from African and Asian football associations" asking him to rethink his decision to step down.
Former FIFA governance adviser Michael Hershman had told ESPN's Jeremy Schaap earlier this month that he was also uncertain that Blatter would walk away.
Former FIFA governance adviser Michael Hershman isn't so sure that Sepp Blatter will actually resign. Sporting Life http://t.co/0n4ohssSgM
- Jeremy Schaap (@JeremySchaap) June 5, 2015
FIFA will set a date for the new presidential election next month. It is expected to take place on Dec. 16, although the European Parliament has urged 79-year-old Blatter to walk away immediately.
However, Schweiz am Sonntag said experts at FIFA doubted whether any of those vying to succeed Blatter, including former Brazil star Zico, could command a majority.
PR consultant Klaus J. Stohlker, who worked as Blatter's personal adviser from January to the end of May, told the newspaper: "It's hard to find someone who is equal to him.
"Blatter has built the organisation into a global, highly successful company, and he's a top diplomat. Blatter has a reasonable chance. It now depends on how he behaves in the coming months."
He added: "Blatter is the elected president at FIFA."
News of Blatter's reported rethink comes just days after FIFA's director of communications and public affairs Walter De Gregorio also announced his resignation from world football's governing body.
The paper reports that De Gregorio had been a leading voice in the clamour for a new start at FIFA, and that his differences with Blatter were insurmountable.
De Gregorio refused to comment when asked about those claims by Schweiz am Sonntag.
Information from the Associated Press was used in this report.