The Red Devils captain has continuously been linked with a move to the Chinese Super League, with their transfer window only closing at the end of this month.
The 31-year-old Rooney has not been a regular starter under Mourinho and the manager has offered no guarantees that his skipper will still be at Old Trafford for the next campaign.
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Mourinho told reporters on Tuesday: “You have to ask him. I can’t guarantee that I’m here next week so how can I guarantee a player won’t be here next season?
“What I can guarantee is that if Wayne one day leaves the club it is not because I want him to leave the club.
“The only thing I can guarantee is that I would never push, or try to push, a legend of this club to another destination.
“So you have to ask him if he wants to stay at the club for the rest of his career or if he sees himself moving on. I’m happy to have him. I have been very open with you. I don’t want him to leave.”