The Blues had two bids for Rooney rejected in the summer and there has been speculation Mourinho is ready to pounce and take advantage to snare the England striker if United fail to qualify for the Champions League at the end of the season.
Asked about Rooney, who is entering the final 18 months of his contract at Old Trafford, Mourinho shook his head and insisted he was not prepared to speak about a player from a team Chelsea are scheduled to face at Stamford Bridge a week on 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 does not anticipate United will struggle to finish in the top four, despite David Moyes' men being five points adrift in seventh with 18 games left this season.
"I don't think they have a problem," the Chelsea boss added.
"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 revealed prior to Saturday's match at Hull, when Chelsea could go top of the Premier League for a few hours at least, that Kevin De Bruyne is nearing a departure with two clubs close to agreeing a fee for the Belgium forward.
There have been "zero bids" for Chelsea's other players, despite rumours of moves for the likes of Spain playmaker Juan Mata, Mourinho insisted.
The self-proclaimed Special One was adamant Eden Hazard will not be leaving Chelsea, amid rumours of interest from Paris St Germain.
The Belgium forward, who joined in the summer of 2012 from Lille, has been Chelsea's best player this season.
If Chelsea were prepared to sell - and Mourinho stressed they are not - a world record fee would be required.
Mourinho 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."
Chelsea have been linked with numerous players during this month's transfer window, despite Mourinho's insistence a deal would be done only in exceptional circumstances and if the timing was right.
Asked if he is interested in Porto striker Jackson Martinez and Inter Milan midfielder Fredy Guarin on Friday, Mourinho responded "no".
Mourinho is hoping to develop his current squad and create a group to rival the one which performed so well for him during his first spell in charge from 2004 to 2007.
Chelsea played Hull in Mourinho's first competitive game of his return on August 18 and played some scintillating football in a 20-minute first-half spell.
Since then Hull have pulled off some good results, particularly at the KC Stadium, where Liverpool lost in early December and Fulham were beaten 6-0 in the most recent home match.
Mourinho was cautiously optimistic ahead of the Saturday lunchtime kick-off, with second-placed Manchester City and leaders Arsenal not in action until Sunday and Monday, respectively.
"A very difficult match to win there," said Mourinho, who is again without midfielder Frank Lampard (calf) and right-back Branislav Ivanovic (knee).
"We have a chance to win. If we win we will be for a few hours top of the league, but I keep saying the most important thing for us is to secure a position in the top four, which is very difficult for everyone.
"As important as that is to improve the team, to improve the players, keep playing well, improving in details and prepare the team for another period of success like Chelsea had between 2004 and 2012."