De Gea made 11 saves in Sunday's 1-0 win over Tottenham Hotspur.
United have triggered a clause that will keep De Gea for another season, but Lingard thinks he deserves a long-term deal.
"He's one of the best keepers in the world, if not the best," Lingard said.
"We want him to stay. Having a keeper like that gives you extra confidence. He's a great goalkeeper."