Solskjaer has not expressed any doubts about his first-choice goalkeeper, but an injury to De Gea's back-up Sergio Romero has made the decision to keep him in the team easier.
"Sergio was injured yesterday so he didn't train. He tweaked his knee. David's been training well this week and will play," Solskjaer told a news conference.
"He's has been fantastic this season. Towards the end he's been in headlines for the wrong reasons but he has to deal with that. The goalkeeping department has experienced better times than just now but David is ready for Sunday."
Solskjaer shifted the focus to the other end of the pitch where United have struggled to find the net in recent games.
"We haven't scored enough, but that happens. When I came in we were very efficient and David was unbelievable at the other end," the Norwegian added.
"Now that fortune has changed a little bit and the margins have gone against us. As a striker and goalkeeper you're always facing little margins and we've been working on creating chances and scoring."
United have already begun planning for next season and Solskjaer said the club had to be prepared to face the prospect of not qualifying for the Champions League.
"In long-term planning we have to think about being in the Champions League next year and the fact we might not be," Solskjaer added.
"You would be surprised how many players' agents have been telling us their players would love to be a part of United in the future.
"That is the lure and the potential and size of the club and we will get back to the good days."
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Toby Davis)
