He has spent the last 11 years of his career in Spain, switching from Villarreal to Atletico in 2010, and has won seven major trophies with the Colchoneros including the 2014 La Liga title.
Having been linked with moves for Harry Maguire, Toby Alderweireld, Jerome Boateng and Yerry Mina this summer, United suddenly began showing an interest in Chelsea's Kurt Zouma late on Wednesday night.
The news comes just hours after manager Jose Mourinho outlined that the club would be making no additions to the squad on transfer deadline day.
Godin, 32, has been one of the world's most consistent defenders over the past five years.
Manchester United have had an approach for Atletico Madrid defender Diego Godin rejected, with the Uruguayan set to sign a new contract with the Spanish club.
United made contact with Atletico this morning about the veteran's availability, but the enquiry was quickly rebuffed.
The Red Devils have found it extremely hard to sign a new center-back this summer as another defender has rejected a move to the Old Trafford.
The 32-year-old was reportedly offered a deal worth £8 million-a-year at Old Trafford but Godin turned down the opportunity in favour of a new contract at Atletico.
The Portuguese has made three signings this summer - Fred, Diogo Dalot and Lee Grant - but has so far been frustrated in his search for a centre-back.
It leaves United going back to the drawing board as they seek a defensive signing today.
"I've been told in the past few minutes Godin's agent was actually the one who approached United this week, saying the player was keen to come to Old Trafford and a deal could be done".