The London club have had two bids for the England international turned down by United this summer and were thought to be preparing a third and final offer before the transfer deadline next week.
However, Rooney received a warm ovation from United fans during tonight's 0-0 draw against Chelsea, and Mourinho vowed to respect the striker's choice should he decide to stay at Old Trafford.
"This club must be a very special club because at every club in the world, when the player wants to leave they don't support him," Mourinho told Sky Sports News.
"When a player wants to leave they give him a hard time but [here] they support him all the way so I think this is a real special club with special fans so he decides that he wants to stay.
"If that is his decision then we will be the first to respect that. It depends on this, it depends on his reaction, it depends on his feelings. If now, he does not want to leave, we are out of the scene - but we need to know what is happening."
Mourinho's apparent desire for a new striker was highlighted in his team selection this evening as he began the match without a recognised frontman.