The most-recent deal De Gea signed in 2015, just days after a proposed £29million move to Real Madrid fell through, runs out next year, although United hold an option to extend that by a further 12 months.
Mourinho regards activating that clause as a foregone conclusion, but also anticipates United offering the 27-year-old fresh terms to ward off any renewed interest from Madrid and ensure he remains at Old Trafford into his 30s.
De Gea joined United in 2011 and has been arguably the club's most impressive player in the post-Sir Alex Ferguson era.
"The option, it's obvious that we're not going to let the option disappear," Mourinho said. "A goalkeeper like he is and obviously a club that wants to be better and better and better, we are not going to let that year option go away.
"But obviously we are going to try (for a new deal).
"Mr (Ed) Woodward is not on holiday. He barely has holidays. Of course he's going to try to give him a contract that keeps him here for much longer than that option that of course we are going to execute.
"I just trust the board and the work they do. I don't negotiate players, I don't discuss numbers and contracts. I just say what is obvious. Anyone of you would say the same - David is to keep."