The Blues had two bids for Rooney rejected in the summer and there has been speculation that Mourinho is ready to pounce for the England international if United fail to qualify for the Champions League at the end of the season.
Mourinho was asked about Rooney, who is currently sidelined with a groin problem, at his press conference ahead of Saturday's Premier League game at Hull.
The Portuguese responded by shaking his head and insisting he was not prepared to speak about a player from a team Chelsea are scheduled to face at Stamford Bridge next Sunday.
"I don't want to speak about it," Mourinho said.
"We play Man United in a few days. I don't think it's nice to speak about a Man United player.
"You have to ask him (Rooney). You have to ask the player. And Man United because Man United has a contract with the player that doesn't end at the end of the season."
Mourinho believes United will still finish in the top four at the end of the season under David Moyes even though they are currently five points adrift in seventh place with 18 games left this season.
"I don't think they have a problem," added Mourinho.
"In this moment they are not top four in the Premier League, but they can be at the end of the season.
"A new manager, but a club with a fantastic culture of supporting the manager.
"I don't feel any problem for David. He works. Better results will arrive and he will be for many years in the club and will reach good results."
Mourinho also insists that Belgium forward Eden Hazard will not be leaving Chelsea amid reports of interest from Paris St Germain.
He said: "I am not worried because if his value was around £40million when Chelsea bought him, if two years later he is twice or three times better than he was when we bought him, I think his value in the market is a crazy value.
"On top of that, he's not a player Chelsea are interested in selling anyway.
"Between our tag of 'not to sell', plus the crazy amount that he can be valued at in this moment, I think there's no chance that Eden is going to leave."
But Mourinho has told Hazard's compatriot Kevin De Bruyne he can leave Stamford Bridge with reports suggesting personal terms have been agreed with Wolfsburg.
"He has a chance to go," Chelsea boss Mourinho said. "We had two bids from two different clubs for Kevin. That's what the club is analysing."