Paris Saint-Germain have also been linked to Oblak, who has been named La Liga's Best Goalkeeper twice since joining Atletico from Benfica in 2014. However, the boyhood United fan's heart is set on a move to Old Trafford.
Oblak has grown discontent at Atletico, and he reportedly wants to leave after a series of broken promises over his future.
The 26-year-old is apparently upset over the club's direction, as Atletico's signings following news of Antoine Griezmann's impending departure failed to convince him of the team's eagerness to win. So far, Atletico have signed Brazilian center-back Felipe from Porto, and striker Nicolas Ibanez from Mexico's Atletico de San Luis.
United failed to secure a Champions League spot for next season. But it's understood the prospect of missing out on the competition doesn't bother Oblak because he's keen on playing in the Premier League.
In April, Oblak said the contract extension he signed, which runs until 2023, is meaningless if Atletico fail to match his ambition.
"I renewed but a new contract does not change anything," said Oblak, according to Pable Egea of Marca.
"As long as Atletico's ambition is the same as mine, I will continue (here)."
The Slovenian, who has a €120-million buyout clause in his contract, is widely regarded as one of the best 'keepers in the world. He recorded 27 clean sheets in 50 matches to end last season.
Meanwhile, De Gea's future at United is uncertain following a mistake-filled season. There's been speculation the Spaniard will leave, with a report in April suggesting the Red Devils were prepared to replace the 28-year-old with Oblak.