The Chelsea manager says any further bids will be made in an official way and insists he will not contact the 27-year-old forward
The London club have seen two bids for the 27-year-old turned down, despite the striker's desire to move to Stamford Bridge this summer.
When asked whether Chelsea are still pursuing Rooney, Mourinho told reporters: "We will try until the last day to add a new player to the squad, a striker.
"But in this moment every striker has a club, every striker belongs to somebody and I don't think it's ethical that I name players that belong to other clubs.
"If we have to make the bid we make it in an official way. We don't speak to players, we speak to clubs.
"We don't try like many clubs do go around and try to influence players to behave in a certain way we go direct to the club in the correct manner and we are going to try that until the last day of the transfer window."
Chelsea got their second era under Mourinho off to a winning start following a 2-0 victory over Hull City Tigers. Oscar and Frank Lampard struck the goals in the first half to secure the three points, and the Portuguese was buoyed by the reaction from the fans at Stamford Bridge.
"The reception was amazing. I was expecting that because I played here with Inter as an opponent and it was fantastic so I could imagine that coming to Chelsea would be like that," Mourinho said.
"When the game started I focused on the game and from now on I think they have to support the team, support the players, bring the players' songs back and support them because I know they like me a lot and they know that I give everything for the club.
"So let's support the team and we need that every game, especially Wednesday because we have a difficult opponent [Aston Villa]."