De Gea, who was at fault for West Ham's goal in United's 1-0 defeat at the London Stadium on Sunday, is in talks about extending his contract at Old Trafford with his deal set to expire in June.
United have the option of triggering an automatic one-year extension until 2024 but sources have told ESPN that club bosses are keen to agree fresh terms on a longer contract which would include a reduced basic wage but with increased performance-related bonuses.
Sources have told ESPN that only minor details are still to be agreed but it's understood the 32-year-old, who has made 540 United appearances for over more than a decade, has been given no guarantees he will be Erik ten Hag's first-choice goalkeeper next season.
The Dutchman will have to prioritise which areas of the squad he wants to strengthen over the summer with United set for a "prudent" approach to the window due in part to concerns about Financial Fair Play compliance.
Ten Hag wants a striker and holds a strong interest in Tottenham Hotspur star Harry Kane and the recruitment team have put together a list of goalkeepers to monitor including David Raya at Brentford and Diogo Costa at Porto.
Henderson has undergone surgery on a thigh injury and won't play again this season but is expected to be fit to return to training in July. The 26-year-old England goalkeeper has a contract at Old Trafford until 2025, although he has attracted interest from clubs in the Premier League and abroad ahead of the summer window.
Despite concerns about De Gea's ability to play out from the back, Ten Hag has not ruled out the possibility of starting next season with the Spaniard as his No.1, particularly if the bulk of his transfer budget is used on other areas of the squad.
De Gea's blunder against West Ham, palming Said Benrahma's tame shot from distance into his own net, has left United just one point ahead of Liverpool in the race for the top four but with a game in hand.
De Gea was also heavily criticised for his performance in the 3-0 defeat to Sevilla last month which saw United exit the Europa League at the quarterfinal stage but speaking at the London Stadium on Sunday, Ten Hag said the goalkeeper still has his backing.
"He has the most clean sheets in the Premier League, so we would not be in this position without him," Ten Hag told a news conference. "So he has fully my belief, no concerns. Mistakes happen, but as a team you have to deal with it, you have to show character, be resilient and bounce back and this team will do."