Ramos is looking to leave Madrid after reportedly falling out with the Los Blancos hierarchy after he was not handed an extension to his current contract, which expires in 2017.
With Red Devils boss Louis van Gaal on the lookout for defensive reinforcements, the Old Trafford outfit have now made a move for Ramos.
According to Sky Sports, Ramos has told Real that he is only interested in joining United, despite reported interest from their cross-town rivals, Manchester City.
There were initially reports that Ramos was using United's interests in an attempt to negotiate a better deal, but it is believed that this is no longer the case, with the 29-year-old determined to leave the Santiago Bernabeu.
Ramos joined Madrid from Sevilla in 2005 and has gone on to make 445 appearances for the club.