The Tampa Bay Buccaneers quarterback, 44, has won seven Super Bowls in an astonishing career spanning 22 seasons.
It was widely reported on Saturday evening that he had decided to retire, but his company TB12 Sports then deleted a tweet confirming the news.
And later, speaking to the NFL Network, Brady's father Tom Brady Sr said his son had not yet "made a final decision".
Brady, a five-time Super Bowl Most Valuable Player, won six titles with the New England Patriots before his final triumph with the Buccaneers last year.
His most recent game was a 30-27 defeat by the Los Angeles Rams in the play-offs, when his heroics narrowly failed to end with the Bucs successfully fighting back from 27-3 down.
Brady, a three-time NFL season MVP, has a year remaining on his contract and has previously talked about playing beyond his 45th birthday, which is a month before the start of next season.
As first reported by ESPN, Brady's decision to retire would be based on several factors, including family and health.
The NFL paid tribute to Brady on Twitter with a series of #ThankYouTom messages.
In a statement to NFL.com, his agent Don Yee said: "I understand the advance speculation about Tom's future.
"Without getting into the accuracy or inaccuracy of what's being reported, Tom will be the only person to express his plans with complete accuracy. He knows the realities of the football business and planning calendar as well as anybody, so that should be soon."
The NFL Network's Ian Rapoport reported that Brady does intend to retire but "the pushback appears to be based on timing, rather than his eventual decision".
Earlier, a post on the social media account of TB12 Sports - the fitness and training company set up by Brady and his personal trainer Alex Guerrero - listed his achievements, and finished: "22 incredible seasons. Thank you for it all, Tom Brady."
Brady has played in 10 Super Bowls, including a miraculous comeback from 28-3 down against the Atlanta Falcons in 2017, and had a perfect 16-0 regular season with the Patriots in 2007.
He won a Super Bowl in three different decades.
Asked about his future after the defeat by the Rams, Brady said: "I haven't put a lot of thought into it. We'll just take it day by day and see where we are at."