Brady's invitation came Wednesday after Beckham commented on one of his posts. The post featured an Aston Martin.
"I'm gonna need a bigger garage," Brady said.
"Waitin for mine too! Sheesh," Beckham commented.
"Come to Foxborough for a test drive," Brady responded.
But Brady's comment to Beckham Jr. was the only one that came with an invitation to the home of the Patriots. Beckham has been linked to trade rumors for the last two off-seasons.
Sources told Pro Football Talk that the Giants "were going to trade" Beckham in 2018 and were listening to all offers. The Patriots were the "most aggressive" team in pursuit of the superstar pass-catcher, according to that report.
League sources told ESPN in March 2018 that the Giants were asking for at least two first-round picks in exchange for Beckham.
Giants general manager Dave Gettleman has insisted that Beckham will not be traded. The three-time Pro Bowl selection signed a five-year, $90 million contract extension in 2018 with the Giants.
Beckham has been in constant communication with Tom Brady for years on Instagram. The NFL stars frequently comment on each other's posts. Beckham, 26, had 77 catches for 1,052 yards and six scores in 12 games in 2018. He drew 124 targets.
Running back James White was the Patriots' leading pass-catcher in 2018, hauling in 87 receptions on 123 targets. He also totalled 751 yards and seven scores. Edelman had 74 grabs for 850 yards and six scores in 12 starts for the Patriots in 2018.
Beckham was working out at the same gym as Minnesota Vikings players Anthony Barr, Eric Wilson and Eric Kendricks on Wednesday in Los Angeles. Beckham's Giants teammate Evan Engram and Pittsburgh Steelers cornerback Joe Haden also were working out at the Los Angeles gym.