Manchester United have made an enquiry about the availability of Diego Godin but are not confident a deal can be done before the deadline, sources have told ESPN FC.
Jose Mourinho is desperate to sign a centre-back and turned his attention to Godin last week.
Sources say United made it clear they would be willing to pay the 32-year-old's €20 million release clause while doubling his salary to €9m a year after tax.
However, they are yet to receive any encouragement from the Uruguay international that he would consider a move to Old Trafford and expect him to sign a new deal with Atletico.
United are not expecting that stance to change before Thursday's 5 p.m. deadline for incoming Premier League transfers and sources have told ESPN FC that the chances of making another signing are diminishing.
Godin, who joined Atletico from La Liga rivals Villarreal in 2010, has just one year to go on his contract with Diego Simeone's side. Sources have told ESPN FC that Godin's sister, who acts as his representative, is in the Spanish capital.
There was a similar situation in the summer of 2015 when Manchester City offered to pay Godin's release clause, then set at €40m. Just days later, Atletico reacted and by offering him a new contract, increased four-year contract.
Transfer news must-reads
- Transfer Talk LIVE: The very latest deadline day news and rumours
- Chelsea make Kepa world's most expensive keeper
- Real Madrid unveil Courtois at Bernabeu
- Kovacic joins Chelsea on season-long loan
- Arsenal to consider Welbeck, Ospina, Elneny offers
- Done deals
Mourinho said on Thursday he is "not confident" of signing a new defender before the start of the season.
Jerome Boateng, Toby Alderweireld and Harry Maguire remain options but sources have told ESPN FC there is an acceptance time is not on their side.
Leicester City manager Claude Puel has warned United that a deadline day transfer for Maguire is impossible, and praised the England international's attitude amid the speculation over his future.
The 25-year-old will be in Leicester's squad for Friday's Premier League opener at Old Trafford and Puel joked: "I can confirm he is going to Manchester but only for a couple of hours.
"I am happy to keep Harry. He is our best player. I am a football manager and I want to keep our best players for the squad and for our season.
"Harry is happy to remain with us. And I am happy with his attitude. He came back with [Leicester and England teammate] Jamie [Vardy] with a smile, with freshness."
He added: "For us it [a Maguire transfer] is not possible. It is not serious. We have to prepare for this season with good possibilities.
"We want to keep good ambition. We lost Riyad Mahrez [to Manchester City], who was a very valuable player for us, so it was important to keep our best players and have good additions to the squad."
Information from Reuters and ESPN FC's Eduardo Fernandez-Abascal was used in this report