Citing sources at Old Trafford, ESPN FC's Mark Ogden reported the Red Devils have begun scouting Oblak more frequently as their concerns over De Gea's future have increased.
United manager Jose Mourinho would prefer to keep the Spaniard at United and has said he will still be at the club in pre-season, but Oblak is his top target to replace him should De Gea move to the Spanish capital.
The 24-year-old has a €100 million (£85.7 million) buyout clause in his Atleti contract, which would make him the most expensive goalkeeper in the world, though his cost would largely be offset by the transfer fee De Gea would bring in, as United will demand a significant sum for him.
Oblak's performances in recent years have firmly established him among the world's best goalkeepers, per Bleacher Report UK's Sam Tighe:
Football writers Andrew Gaffney and Ryan Baldi also believe he would be the outstanding choice to replace De Gea should he leave:
The Slovenia international is one of the few goalkeepers on a similar level to the Spaniard, and as such, his arrival to replace De Gea would ensure a smooth transition.
He's already an experienced campaigner, and prior to joining Atletico, he helped Benfica win a domestic treble and reach the Europa League final in 2013/14, keeping 22 clean sheets in 28 matches in the process.
With Atleti, he has garnered experience at an even higher level and played in last year's UEFA Champions League final.
Per beIN Sports' David Cartlidge, while Oblak benefits from having an excellent defensive unit in front of him, he still shines through as a fantastic stopper:
Oblak is strong and confident in the air, so he should be well-suited to the rigours of Premier League football, and his reflexes and shot-stopping are remarkable, even for a 'keeper of his considerable standing.
Prising him away from Aletico won't be cheap or easy, but if there's one player who can ensure De Gea wouldn't be missed at Old Trafford, it's Oblak.