Mauricio Pochettino is reportedly interested in recruiting the former Real Madrid captain, whose shocking Bernabeu exit was announced this week, according to RMC.
Ramos, on the other hand, is seeking a two-year deal with weekly salary of £200,000.
United might potentially be in pole position to sign the veteran defender after he turned down a bid from previous club Sevilla.
Ramos is thought to be the ideal complement for Manchester United captain Harry Maguire.
And United has already demonstrated that they are not hesitant to provide huge contracts to the right player.
Ramos joined Real for £23 million from Sevilla in 2005 and played 671 times for the club, scoring 101 goals in 16 years. Real won five LaLiga titles, four Champions Leagues, and two Copa del Reys during his tenure.
Despite missing out on Spain’s Euros team, Ramos remains the most capped player in the country’s history, having played 180 times for his country.