Speaking after his team's 2-1 win over Villa on Wednesday, Mourinho said there would be another bid for Rooney, but not before Chelsea visit Manchester United on Monday.
"We want to do something with Rooney," Mourinho said.
"But we will be ethical and not interfere with Manchester United by bidding on him before we play them next week; the board agrees with me on this."
Chelsea needed a 73rd-minute headed from Branislav Ivanovic to claim three points against Villa at Stamford Bridge.
Antonio Luna's own goal had given the hosts the lead before Christian Benteke levelled for Paul Lambert's men on the stroke of half-time.
Lambert slammed referee Kevin Friend for not sending off Ivanovic before his goal for an apparent elbow on Benteke and failing to award his team a penalty after John Terry handled in the area.
Mourinho praised Friend for the way he handled the physical battle between Ivanovic and Benteke but suggested a draw may have been a fairer result.
"This is English football, for some reason the world loves it more than any other league; one thing is (because of) a real aggression I would call it," Mourinho said.
"Another thing is duels that are handled in a certain way and I think the referee did very well. From minute one to minute 95 there was a real fight; a football fight between Benteke and Ivanovic.
"A draw wouldn't have been an unfair result. They fought a lot. They created great difficulties."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.