De Gea was left out of the squad for United's Premier League encounter with Southampton on Wednesday - with stand-in keeper Sergio Romero in outstanding form to help Mourinho's men claim a 0-0 draw.
Romero has already been guaranteed his place in United's starting XI in their Europa League final against Ajax on May 24, and Mourinho revealed in the pre-match build-up that third-choice shot-stopper Joel Pereira is likely to feature against Crystal Palace in the final Premier League clash of the season.
That news did little to quell rumours of De Gea's imminent departure, with his appearance against Tottenham last time out possibly his final in a United shirt, but Mourinho moved quickly to confirm the Spaniard is still firmly in his plans.
"[When will] David [play]? I think the first match against LA Galaxy in pre-season," Mourinho told BBC Sport.
"I hope to play Joel Pereira against Palace and Sergio in the Europa final. David is top of the world and obviously we want to keep him."
Romero was on top form at St Mary's Stadium, an early save from Manolo Gabbiadini's penalty setting the tone for a superb display.
United's chances were few and far between, though Anthony Martial did rattle the woodwork midway through the second half.
And Mourinho said that, despite an imperfect display, he was pleased with his side's desire to prove themselves ahead of the Ajax clash - signalling out Romero for individual praise.
"We played a good team, a team who tried to win and tried to finish well. I think we did more than ok," Mourinho added.
"I think all of them gave me positive feelings. Sergio had a very good performance, more than very good.
"The team wasn't perfect but individually they gave me good things. They showed me they want to be an option for the final."
17 - Even if Man Utd win their remaining game, it will be their lowest ever total of wins in a single PL season (currently 17). Drawn.— OptaJoe (@OptaJoe) May 17, 2017
Southampton boss Claude Puel - whose future on the south coast has been called into question -meanwhile, was left to rue his side's failure to make their domination pay.
"It's a shame our performance was not enough in the first half. But in the second half in terms of opportunities, we deserved to score and had seven or eight shots on target," Puel said.
"We needed to be clinical perhaps, but we played good football and had chances to win the game.
"It's a third penalty miss. It's very important as it can give confidence and we needed confidence at the beginning of the game. It's a problem perhaps for us but in the second half I'm happy with our comeback."