The 41-year-old quarterback made the comments at the Super Bowl opening night event on the NFL Network on Monday.
Brady and Talib are former New England Patriots team-mates, with the 32-year-old defensive player spending a year and half in Boston back in 2012 and 2013.
Talib was traded to the Patriots from the Tampa Bay Buccaneers, along with a seventh-round draft pick and the Patriots gave up a fourth-round draft pick themselves as part of the deal.
“The day that we got him, Bill Belichick brought him over to see if he could play receiver,” Brady explained.
“After practice.”
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“He got me all excited, I thought I was going to have a receiver package,” Talib said interrupting.
“Tom was throwing me passes.
“So, I can say I caught passes from Tom Brady though.”
Talib’s performances for the Patriots back in 2013 were good enough to see him get a Pro Bowl and All-Pro Team call-up, both of which were the first of his career.
The veteran cornerback clearly made an impact on Brady despite his short time at New England.
“He could have been as good a receiver, as he is a corner,” Brady said about Talib.
“A great athlete.”
Ahead of their showdown on Sunday, the Rams have four players on their roster who have participated in a Super Bowl, one being Talib, while the Patriots have 36 players with Super Bowl experience.
Talib, who won he ring with the Denver Broncos in 2015, was asked if he had any advice to his Rams team-mates.
“Advice is not going to get you too far in this game,” Talib said.
“You got to just prepare and show up at the game and play football.
“You have to play football at the end of the day.”
The Patriots will face the Rams on Sunday in Super Bowl LIII, with the game played at the Mercedes-Benz Stadium in Atlanta, Georgia.