Sources told Pro Football Talk that the Giants "were going to trade" Beckham last year and were listening to all offers. The Patriots were the "most aggressive" team in pursuit of Beckham, according to that report.
Beckham has been in communication with Tom Brady through social media for years, with the superstars frequently commenting on posts.
Beckham wrote "love you brother" on Brady's most recent Instagram post.
Sources told Pro Football Talk that the 49ers remain interested in renewing their pursuit of Beckham this offseason.
League sources told ESPN that the Giants were asking for at least two first round NFL Draft picks for Beckham in March 2018.
Beckham, 26, signed a five-year, $90 million contract with the Giants in August. He has a $16.7 million base salary in 2019. The three-time Pro Bowl selection had 1,052 yards and six scores on 77 receptions in 12 games in 2018, while limited by a quad injury.
The No. 12 overall pick in the 2014 NFL Draft has 5,476 yards, 44 touchdowns and 390 receptions in 59 games during his NFL tenure.