The Spaniard, 28, made 11 saves as United beat Tottenham 1-0 at Wembley.
During 11 years as a striker at Old Trafford, Solskjaer played alongside Edwin van der Sar and Peter Schmeichel.
“We’ve had some great keepers at this club and I think he’s challenging both Edwin and Peter for the number one spot historically,” Solskjaer said.
De Gea’s 11 saves was his highest in a Premier League game while also keeping a clean sheet and helped United make it six wins from six under Solskjaer.
The Spain international joined United from Atletico Madrid in 2011 and has won the club’s player of the year award in four of the past five seasons.
“He should have held a couple,” joked Solskjaer. “We had a good back four and David in behind them was unbelievable. You are allowed to have a good goalkeeper.
“I’ve played with a few fantastic goalkeepers. We have a tradition of having them and he has grown and grown. He deserves that man of the match today.”