The Spanish international is out of contract at the Santiago Bernabeu at the end of the season, with talks over an extension rumoured to have stopped progressing in recent weeks.
That lack of clarity over his future has opened up speculation the 34-year old could end his 15 year stint in the Spanish capital in the coming months.
According to reports from the Daily Mirror, United have now signalled their interest in making a free transfer offer, alongside Ligue 1 giants Paris Saint Germain.
Ramos is now free to negotiate a pre-contract move to a non-Spanish club, with moves to Asia and the USA apparently not an option.
Any interested club is likely to have to agree a wage reduction in order to secure an agreement, with Ramos likely to be forced to take a cut from his current €10m annual salary.