The London club have made two unsuccessful bids for the England striker and have not ruled out making a third with their pursuit of him coming after former United manager Alex Ferguson said in May that Rooney wanted to quit Old Trafford.
Rooney played the whole of Monday's 0-0 draw at home to the club chasing his signature with his manager David Moyes saying his performance on the pitch demonstrated his position on the matter without him actually needing to say it.
"I think the person that started the story has to finish the story," Mourinho told a news conference.
"A club like us, a manager like me and the people that work in the club with me, we are not silly to try to get a player from a big club, a club that does not sell what they don't want to sell, we are not silly to try something if somebody didn't start," he said.
Asked if he meant did he want Rooney, who has not commented on the matter publicly, to come out and say he wanted to stay or go, he replied: "Yes."
Rooney, who was cheered by his own fans and Chelsea's, who were singing "Wayne Rooney, we'll sign you next week", had the best goal-scoring chances in a poor game, including an attempt at an acrobatic volley in stoppage time.
"I think his performance tonight said enough, he closed two or three people down in the corner and I think the crowd realised the work he did," said Moyes, who has faced a barrage of Rooney questions since taking over the job last month.
"He was desperate to score, you could see that by the way he nearly scored with an overhead kick in injury time. So I think his actions tonight showed what he thought," Moyes added.


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