The Spain international is leaving Real Madrid after 16 successful years at the Bernabeu.
RTVE journalist Jose David Lopez reports United have made contact with Ramos about a blockbuster move to Old Trafford.
“ManUnites (sic) is one of the clubs that has already contacted Sergio Ramos," he said on Twitter.
“He handles several offers, but he is highly valuing the project in which he falls, because he wants to go to a club that continues to compete to win Leagues and [the] Champions [League].
“If, in addition, it can offer you a 2-year contract, ideal."