With the Europa League final providing a path into next season's Champions League the game could define whether Mourinho's season at United can be regarded as a success or failure.
De Gea was left out of the United squad which drew 0-0 with Southampton at St Mary's and is not expected to play again this season.
Manchester United will look to avoid picking up any further injuries when they take on Crystal Palace at Old Trafford on Sunday afternoon.
"In any country in the world, it would be Saturday".
"The only positive is for me to save my players and give him the opportunity for Wednesday".
Asked if he had submitted a request for the game to be moved, Mourinho replied: "I don't lose time".
"I know some people like to lie". I'm here already, four plus three, seven years. I never look at coaches from other teams.
"I never saw that with Chelsea, I never saw that with Manchester United, I never saw that with Manchester City previous year".
"Smalling has a problem, a small problem that I think it is no problem for next week, but is a problem for the weekend. We have to accept the way it is".
Mourinho rested a number of first-team stars with next week's Europa League final in mind.
He said: "We will have two keepers, Joel Pereira and Kieran O'Hara, and we will have Demetri Mitchell, Scott McTominay, Matty Willock, Josh Harrop, Angel Gomes, Zachary Dearnley, Axel Tuanzebe, so lots of them. I think we did more than OK", Mourinho said. It will be a big occasion but I think the best for the young player is in the middle of an experienced structure, where he can be supported.
"I hope he tells Wilfried Zaha to go slow and leaves Christian Benteke at home". I'm working hard every day and the next step is on Sunday, so let's focus on that and we will see.
Eric Bailly is nearly certain to start as he's suspended for the Europa League final while Timothy Fosu-Mensah is set to return after recovering from a shoulder injury.
Marouane Fellaini came off rubbing the back of his right thigh against Southampton, but Mourinho said the Belgian midfielder was confident he had not torn his hamstring.
Southampton sits eighth with 46 points, and finishes the season at home Sunday to Stoke City. "We have a very good relationship and, when it's the right time, we have fun as well".