The Blues have already seen two offers for the England international turned down prompting Mourinho to wait and see where Rooney sees his future before lodging a third proposal.
Rooney was solid as he started for United in Monday night's 0-0 draw with Chelsea at Old Trafford and Mourinho is now under the impression that perhaps he could remain with the reigning Premier League champions.
"First, we have to speak," he told Sky Sports.
"I think this club must be a very special club because at any club in the world when a player wants to leave, they don't support him. When a player wants to leave, they give him a hard time, but they support him all the way.
"I think this a special club, with special fans, and if he makes that decision, we will be the first to respect that and to say it is over."
Mourinho added further: "It depends on this. It depends on his reaction, on his feelings.
"If now he doesn't want to leave, we are out. We need to know what is happening."