But Mourinho denied that any Chelsea players were offered to United in part-exchange for Rooney and stressed that his club had made the offer in the correct manner.
Chelsea lodged a written bid for the England international on Tuesday, which has been rejected, and reports surfaced on Wednesday suggesting the bid was £10m plus Juan Mata or David Luiz.
But Mourinho reiterated Chelsea's earlier denial that any players were involved in their offer when he said: "Chelsea is interested in this player, made a bid, and what we did, we did officially.
"The bid is there. The club knows we want the player, the player has to know we made a bid for him.
"Now we have nothing more to say. We want the player, we made the bid and now it is up to Man United and we respect their decision.
"We don't want to make public the bid but it is just a certain amount of money and it doesn't involve players or players in the possibility of negotiation. No Juan Mata, no David Luiz.
"I work with my players now, as I've done from day one. I trust my players, I'm happy with them, and that's what I have to do now.
"We did what we had to do in a proper way, in an ethical way, and we're very happy with our behaviour. It was clean.
"Now I keep doing what I'm doing, working with my players, trying to improve my players, and we'll see what happens. Now he's with Man United, not with us.
"From me no more comments with respect to Man United, my colleague (United manager) David Moyes and my players."
Mourinho did confirm that Rooney is Chelsea's only current transfer target.
Asked if it was a case of Rooney or nothing, he said: "Yes."
Since taking charge at Manchester United, Moyes has been adamant that Rooney is not for sale and he said recently: "Unless I was speaking Double Dutch last week, we said Wayne Rooney is not for sale.
"It's hard to keep repeating myself but I will. Wayne is a Manchester United player and it will remain that way."
Angry and confused
However, news of Chelsea's bid for Rooney followed the revelation that the 27-year-old is 'angry and confused' about further remarks made by Moyes, which could be seen as implying that he is not a first-choice player at United.
Moyes said: "Overall, my thought on Wayne is that if, for any reason, we had an injury to Robin van Persie, we are going to need him and I want as many options as possible."
Rooney, who has flown home from United's pre-season tour because of a hamstring injury, has two years left on his United contract and is also reportedly unhappy that chief executive Ed Woodward has publicly ruled out negotiating an extension.
Woodward has cut short his stay at United's pre-season tour to Sydney in order to return to Europe on urgent transfer business although indications are the business does not revolve around Rooney.
Arsenal boss Arsene Wenger is hopeful of persuading Rooney to move the other way, insisting the Gunners have the finances to do so.
"Rooney is under contract and has two years to go so it's United who make the decision," he was quoted in the Sun.
"But we would not have a problem with the wages of Rooney."
If Woodward is not dealing with the fall-out from the Rooney affair, the chances are he is trying to progress the transfer of Cesc Fabregas.
United remain confident of securing the services of Fabregas despite Barcelona's insistence the player wants to remain at the Camp Nou.
Senior figures within the Red Devils camp are of the opinion Fabregas wishes to join them, although it may take more than the £25million they bid for the player earlier this week to persuade Barcelona to accept.
Even this situation is not straightforward given Fabregas has a clause in his contract which would ensure Arsenal were made aware of any developments.
Yet, speaking on his own club's tour of the Far East, Wenger made it clear he thinks there will be none.
"At the moment, Fabregas has decided to stay one more year at Barcelona," Wenger said.
"We have the clause in the contract so we would be on alert but at the moment that is not something we are after."