The goalkeeper is approaching the end of his current deal and could leave Old Trafford for free at the end of the season.
United, however, believe they are close to an agreement which would see De Gea extend his stay while taking a cut in his basic wage but with larger performance-related incentives.
Most of the terms have been finalised although talks are continuing about how the contract is structured.
United also have the option of triggering a one-year extension to his existing deal which is valid until May, but there's confidence at the club that fresh terms will be in place before that's necessary.
De Gea has been Erik ten Hag's undisputed No.1 since the Dutchman's arrival last summer, making 47 appearances in all competitions.
The 32-year-old has made more than 500 appearances since arriving from Atletico Madrid in 2011. He has won United's player of the year award four times and lifted the Premier League title, FA Cup, League Cup and Europa League during his 12 years in England.
Sources have told ESPN that United continue to monitor a number of goalkeepers ahead of the summer transfer window but Ten Hag's priority is to land a top-class striker. There is also interest in midfielders Frenkie de Jong and Jude Bellingham.
The Portugal full-back is under contract until 2024 after United triggered a one-year option in December but the club are keen to put a longer agreement in place. The 24-year-old has made 35 appearances so far this season and has been linked with a move to Barcelona.
Marcus Rashford's new contract is also a priority. Sources have told ESPN that negotiations with the England forward have not been affected by uncertainty over the club's ownership situation and that there is confidence on all sides that a new deal will be agreed.