Martial, who joined United from Monaco in 2015, recently rejected an offer to extend his contract, but remains in talks with the Premier League giants.
Mourinho was said to be willing to sell Martial in the summer, but the 22-year-old has enjoyed a promising start to the new campaign, scoring four goals in his last three league games.
When asked during his press conference on Friday if he is confident that Martial will stay, Mourinho said: “I don’t belong to the discussions of contracts.
“I don’t even know their contracts in the sense of numbers and I’m really happy with that – to not have to participate in these types of discussions.
“Obviously I hope we will agree. He is a talented player – everybody has known that since he was at Monaco.
“Another thing is a talented player with consistency and understanding what a football match is in the globality.
“When you reach that level or are almost reaching that level is when you become a top player. One thing is a top talent, another thing is a top player.
“When he is now much closer to becoming a top player, obviously I would like him to stay. I know the club very much wants him to stay so hopefully he is going to stay.”