The 27-year-old is widely considered to be the world's top goalkeeper and kept 18 clean sheets in the Premier League before being named the club's best player for the fourth time.
Mourinho said: "He is a Manchester United player and will as soon as possible sign a new contract.
"Would I swap De Gea for any other keeper in the world? No.
"He likes it here, we love him.
"We want him to stay, so when a player is not on the market his value is zero."
Long-term suitors Real Madrid bagged Thibaut Courtois from Chelsea in a £38million deal on transfer deadline day, ending speculation linking De Gea to the Bernabeu.
The Spaniard was part of the United squad that flew south for their Premier League clash against Brighton this afternoon.
He endured a difficult World Cup as Spain crashed out on penalties to Russia and their defence let in six goals during the tournament.
But he was part of a top Red Devils defence last term — and Mourinho will hope he can keep it up with the Victor Lindelof and Eric Bailly partnership starting to blossom.
Mourinho also compared his behaviour to that of Paul Pogba, whose agent Mino Raiola appears to have rocked the boat in a bid to get his client a better deal.
The Portuguese added: "I think there was a collective situation involving the player, the agent and Manchester United.
"The agent didn't create a war to achieve his objectives.
"He respected the club. He respected the player. The player was always keen to stay and happy to stay.
"The club understood how important he was and was always trying to give him the conditions to make him happy, so credit to all three."
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