Brady -- rocking a grey hoodie and jeans -- showed up at Funke restaurant with the famous sideline reporter and other Fox Sports colleagues around 10 PM Monday night ... and the group quickly entered the venue with security in tow.

We're told the future Hall of Famer and EA wanted to meet up to discuss Brady's upcoming color commentary gig with Fox Sports ... which officially starts in 2024.

Of course, Andrews has been with the network since 2012 ... leading the sideline for its main broadcast team and reporting for the biggest games on the schedule.

Brady's going into next season as a rookie after inking a 10-year deal worth hundreds of millions of dollars.

We're assuming Brady picked her brain throughout the dinner ... considering she's a seasoned vet at this point.

There's a chance the two may have also talked some Taylor Swift and Travis Kelce ... considering the Kansas City Chiefs superstar credits EA with setting up the power couple.