Manchester United insist Rooney is not for sale and he was outstanding as the sides played out a draw on Monday.
"The person that started the story has to finish the story. For the good of everyone it is time to finish the story," said Jose Mourinho.
"One way or another he has to say 'I am ready to leave' or 'I want to stay'."
He suggested the 27-year-old striker himself was the reason for Chelsea's move saying "he told someone very important in his career" that he wanted to leave United.
Asked how long he was prepared to wait before moving on to other targets - with Anzhi Makhachkala's Cameroon striker Samuel Eto'o understood to be the alternative - Mourinho replied: "Twenty-four hours, 48 hours."
He added: "If you look at a manager like
me, a club like us and the people who work at the club with me, we are
not silly enough to try and get a player from a big club that doesn't
want to sell.
"We are not silly enough to try something if somebody didn't start it."
He added: "After that, if he wants to leave he has to say - or if he has decided now he doesn't want to leave any more then he has to say."
The former Everton forward was given huge support throughout by United's fans and indeed Chelsea's supporters who want him to switch to Stamford Bridge.
The Blues boss said: "He was a real professional. He played for his club, the club that pays him, and tried to win.
"He tried to score. He played a fantastic match in difficult circumstances and I praise him. You have to say it was fantastic because many players in this situation can't express themselves."
Mourinho also praised the support Rooney received from United's supporters, saying: "It was fantastic. In other countries it would not be possible. It was very English."
He also dismissed speculation that Juan Mata, left on the bench at Old Trafford, would be sold as he said: "He is very important to Chelsea and the stories coming out are nonsense. No chance - Juan goes nowhere."
[BBC]