The Stamford Bridge outfit were the subject of a failed offer for the England international on Tuesday, with reports suggesting defender David Luiz or midfielder Juan Mata were offered as part of the deal.
While admitting an bid had been lodged, Mourinho denied claims of a part-exchange deal and insisted Rooney's future now lies with him and his current employer.
"Nothing is secret anymore. Chelsea are interested in the player, Chelsea made an official bid," the Portuguese said.
"What we did, we did officially, in a clean way. There is nothing more to say and nothing more to do.
"We want the player, we are interested in the player and we made the bid.
"Now we have to respect Manchester United and be ethical in this process so no more comments. From now on I don't say one more word about Wayne Rooney because we all know we want him. It's up to Manchester United and up to the player.
"No players are involved, no David (Luiz), no (Juan) Mata and no possibility of a player involved in our bid.
"We don't want to make public what has to be private which is the official bid we made.
"The official bid is about a certain amount of money, it doesn't involve players and doesn't involve players in the possibility of the negotiations continuing."
Rooney, who handed in a transfer request at the end of the season, is thought to be disillusioned at Old Trafford following suggestions by new manager David Moyes that Robin van Persie would be the club's number one forward under his leadership.
Arsenal are also reported to be interested in buying him, although a switch to Chelsea is thought to be his preferred move.