Brady claimed six Super Bowls with the New England Patriots before bagging a seventh with Tampa Bay Buccaneers following shock move to Florida in 2020.
The 44-year-old is regarded as one of the greatest ever players and tops the charts in almost every single passing statistic.
Despite the reports, Brady's agent Don Yee insisted "Tom will be the only person to express his plans", adding that he expects a statement to come "soon".
A post on the Twitter 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, @TomBrady."
That tweet has since been taken down, but there has been no comment from Brady himself or the Buccaneers.
A statement from Yee, posted on the NFL website, read: "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."
Former Patriots receiver Julian Edelman, who caught 41 touchdown passes from Brady across the regular season and post-season, greeted the initial reports by tweeting: "Thanks for the memories, babe."
He later added: "Can't a guy thank another guy for the memories without everyone thinking he's retiring!?"
Brady had hinted at retirement in recent days when he noted that the feelings of his wife - supermodel Gisele Bundchen - and their family would play a part in his decision.
"I have kids now and I care about them a lot," Brady said on Monday on his Let's Go podcast, following Tampa's play-off exit against the Los Angeles Rams the previous day.
"My wife is my biggest supporter. It pains her to see me get hit out there. And she deserves what she needs from me as a husband and my kids deserve what they need from me as a dad."