Spaniard De Gea, 20, has enjoyed mixed fortunes since arriving from Atletico Madrid this summer in an £18.3m deal, while Lindegaard has piled the pressure on his rival.
Lindegaard said: “I got a stamp on my ankle at the start of the match on Saturday and should have come off.
“I chose to carry on and paid the price. And although I have to sit on the couch with my leg up now, it was incredibly important to me to play.
“The medical staff at United believe that the earliest I could train again is next week.”