Ramos' contract with Los Blancos is set to expire at the end of the season, but despite having opened talks with the club over a new deal, he has been strongly linked with a move away from the Santiago Bernabeu.
The 34-year-old was widely expected to sign a new two-year contract, but those plans could have changed after his former teammate Beckham, who is the founder and co-owner of MLS side Inter Miami, reportedly indicated an interest in acquiring his services.
According to Spanish publication AS, the former England international has handpicked Ramos to be his side's latest acquisition, following the big-name signings of Gonzalo Higuain and Blaise Matuidi from Juventus earlier in the year.
It is also claimed that Ramos is unlikely to make the switch as he is still competing at a high level with Real and the Spain national team, but would be interested in moving to Miami as his career draws to a close in the coming years.