A leader and a champion defender, Godin has a huge admirer in Manchester United manager Jose Mourinho.
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.
The Portuguese is desperately seeking reinforcements for his defence on the eve of the campaign with summer-long interest in Toby Alderweireld and Harry Maguire failing to result in moves ahead of deadline day.
Godin, the captain of the Uruguay national side, is widely considered to be one of the best defenders in the world, and at 32, has plenty of experience.
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.
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Speaking on the BBC's World At One, the MP for Beaconsfield said: "If he was to become leader of the party, I won't be in it". She said: "I know that many people have found this offensive".
Reports have also suggested Godin has a release clause in his Atletico contract worth just £18m.
Now that the Godin deal has fallen through, it looks like United won't be signing any new central defenders before this evening's 5pm deadline - a position Jose Mourinho has seen as a priority to strengthen.
United were hopeful that they could have persuaded Godin to sign and join his new teammates in time for the Red Devils' Premier League season opener against Leicester on Friday night but they will have to return to the drawing board now.
United have signed three players this transfer window, Diogo Dalot, Fred, and Lee Grant.
A leader and tough uncompromising defender, he is a player Mourinho has coveted for some time and is a key component to Atletico where he has a strong relationship with coach Simeone and that relationship has led to a deadline day rejection.