United boss David Moyes appeared open to rewarding the Spaniard with a new and improved contract. Reports have suggested De Gea is the next in line for a new deal after impressing in recent weeks.
Wayne Rooney recently signed fresh terms, committing his future to the club, and David Moyes is keen to tie down his top first-team stars as soon as possible.
"David De Gea has been terrific," Moyes said. "He has been great. He came in as a good young goalkeeper and he is turning into a great goalkeeper with a lot more to come."
The former-Atletico Madrid keeper was heavily criticised in his first season at Old Trafford, but has since established himself as one of the best young goalkeepers in the world.
Speculation has continually linked with a return to Spain, with Barcelona and Real Madrid the two most commonly linked.
Barcelona are set to lose Victor Valdes at the end of the season, with the Spain international ready for a new challenge. Real Madrid, meanwhile, have rotated by between Iker Casillas in the Champions League and Diego Lopez in La Liga.
But Moyes wants to keep him at Old Trafford if possible - which would suggest a new deal is in the works.
"The club are always going to keep their best players," Moyes said. "The club will always look to keep the players who they feel they need to."