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.
However, Atletico are unlikely to let their captain leave at this late stage of the summer and there are question marks over whether Godin would want to leave the Europa League holders, where he has spent the last 8 years of his career.
"I'm not confident, I'm not confident and the market closes today so is time at least for me to stop thinking about the market because the market will be closed", he told reporters when asked about his transfer options.
The newspaper also claimed United have contacted Atletico, with Mourinho determined to bring in one more signing. "I will have to focus on the players I have in relation to this first couple of matches".
The situation all seemed rather complicated until Sky Sports cleared up the situation and it seems Godin's agent used United to bag a pay-rise and new contract. However, the 121-time capped Uruguayan worldwide feels settled in the Spanish capital and enjoys an excellent relationship with his current boss Simeone, which has led to him rejecting the English giants' overtures.