The Blues have already had two bids for Rooney rejected by United, with David Moyes insisting the striker is not for sale at any price.
Chelsea are set to test that resolve once more, perhaps even before the trip to Old Trafford next Monday if Mourinho is feeling mischievous.
"We will try till 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," said Mourinho, following Chelsea's 2-0 defeat of Hull on his return to Stamford Bridge on Sunday.
"We don't try, like many clubs do, to go around and try to influence players to behave in a certain way.
"If we have to make a bid, we make it in an official way, we don't speak to players, we speak to clubs."
The self-proclaimed Special One was enthused by the first-half performance, in particular, on his homecoming.
Goals from Oscar and Frank Lampard, who also had a penalty saved, saw Mourinho's men triumph in an incident-packed match which saw goal-line technology employed in the top-flight for the first time when Allan McGregor saved from Branislav Ivanovic.
"I played so many times here, I won so many matches here, but we didn't have so many periods of such fantastic quality like we had (against Hull)," Mourinho said.
"I'm happy we managed to win and we managed to show that this is the football we want to play, this is the football we can play.
"Now it's up to us to make it happen more times and more times during the game."
Mourinho, who left Chelsea in September 2007, returning to win with Inter Milan in March 2010, described his reception as "amazing" before calling on supporters to throw their energies behind the team in Wednesday's Premier League clash with Aston Villa.