The 31-year-old, who has been left out of the Spain squad for the 2022 World Cup, will soon enter the final six months of his contract at Old Trafford.
The Red Devils have the option to activate a further 12 months, but there has been speculation surrounding his future, amid claims that head coach Erik ten Hag wants to bring in a new number one.
According to the Daily Star, De Gea's form this season has convinced Ten Hag that he is capable of still performing at the highest level, with the club's head coach keen to keep hold of him.
However, the report claims that the Spaniard would have to be prepared to take a significant wage reduction, with the club not willing to extend the deal on his current salary.
De Gea is said to collect in the region of £375,000 a week, which makes him the second-highest earner at the club behind Cristiano Ronaldo, who is set to leave on a free transfer next June.
The experienced goalkeeper would allegedly have to agree to reduce his salary by around £100,000 a week in order to remain at Old Trafford, which would save the club around £5m per year.
There has reportedly not yet been discussions between the club and De Gea's representatives, but there could be talks over the break for the World Cup, with De Gea not selected for Spain.
The stopper has made 19 appearances for the 20-time English champions during the 2022-23 campaign, keeping nine clean sheets in the process.
Meanwhile, since arriving from Atletico Madrid in July 2011, he has represented the club on 506 occasions, which has included 390 appearances in the Premier League.
"It is clear already and I have already emphasised it several times, I am really happy with David. He is a great goalkeeper," Ten Hag told reporters after De Gea's strong performance against West Ham United at the end of October.
"He is only 31. He is fit. He can progress even more. He was already impressively good for Man United and I think he will do that in the future as well.
"Everyone has his own opinion but for me, the first thing for a goalkeeper is to protect the goal and make sure you don't concede goals. In that fact he is magnificent.
"But with the feet he has capabilities as well. That is not only with the keeper but also the one in front and what options you give to bring passes in. I am convinced he can do it. The games so far he proved it."
Diogo Costa has been linked with a move to Old Trafford in recent months, but Portugal's goalkeeper has just signed a new long-term contract with Porto.