De Gea, who joined United in 2011 when Alex Ferguson was manager, is the current squad's longest-serving player having made nearly 550 appearances for the club.
"David De Gea's contract is due to run out but discussions remain open with the long-serving keeper," United said in a statement.
De Gea won his second Premier League Golden Glove last season after he kept 17 clean sheets but the four-time club player of the year has come under the microscope for his shortcomings and errors in recent years.
The shot-stopper is one of the highest-paid players at the club according to British media but has not featured for Spain since 2020.
The BBC reported that De Gea is getting married this weekend and any new deal will not be signed until he resumes face-to-face talks at United.
United have also been linked with a move for Inter Milan goalkeeper Andre Onana (27).