Inter Miami are set to enter MLS in 2020 and are looking for a big-name signing, with Messi undoubtedly the biggest of the names linked.
Messi has recently been linked with a future move to MLS, following the revelation that he has a clause in his current contract which would allow him to leave Barcelona at the end of this season.
According to the report from Spain, Barcelona is aware of the approach by Beckham. The Barcelona board, it was recently reported, want to sign Messi to a lifetime contract.
This all comes just days after Messi said in an interview with Sport that he wanted to remain at Camp Nou for "as long as possible".
However, the 32-year-old also hinted that his commitment to the club is contingent on winning titles: "I need to see there's a winning team because I want to keep winning things at this club.
Set to join the league in 2020, Beckham's team have started making their first signings, and have been linked with big-name stars such as Messi's Barcelona teammates Luis Suarez and Antoine Griezmann, PSG's Edinson Cavani and Mauro Icardi among others.