Rooney has been the subject of two bids from Chelsea, both rejected by United, and remains Mourinho's priority target before the closure of the summer transfer window on September 2.
Ahead of a return to the Barclays Premier League, his favourite competition, against Hull on Sunday and asked specifically about whether Rooney will soon be playing in the blue of Chelsea, Mourinho was non-committal.
"I'm just a Chelsea manager, as every one of us (managers) looking always to try to strengthen your squad," Mourinho said.
"We all say no, but we lie. Until the last day when the market is open, we all are waiting for something to happen.
"Even when we say we're very happy with our squad, we lie, because we want always to make it better.
"We will see what happens, not just with us, with Man United, with everybody else, and see if we can improve our squad, a squad that I like.
"I'm not lying when I say I like (the squad), and I'm not lying when I say I'm enjoying very much to work with these young people, some of them first steps in the Premier League."
Mourinho again insisted David Luiz is not for sale amid interest from Barcelona in the Brazil defender.
The former Real Madrid boss added: "We want to keep him and we understand that a big club like Barcelona wants the best and tried to get one of the best central defenders in the world, but we are being very honest also by saying there is no chance David is leaving."
Luiz last season established himself as a key figure in the Blues squad, which features an experienced core of Petr Cech, John Terry, Ashley Cole and Frank Lampard as well as numerous young players brimming with talent, but some lacking Premier League experience.
Mourinho has never suffered Premier League defeat as Chelsea boss at Stamford Bridge - a run of 60 games - and will return as an English top-flight boss following a gap of 2,164 days since the 0-0 draw with Blackburn in September 2007.
While the Portuguese, who signed a four-year contract in June, knows the stadium well, new signings Andre Schurrle and Marco van Ginkel do not.
Mourinho will take his squad to train at Stamford Bridge on the eve of the Hull contest, so they can experience their surroundings before the competitive action begins.
The Portuguese, who returned to Stamford Bridge with Inter in March 2010, will also take the opportunity to savour his surroundings ahead of an expected emotional return to a club where he is adored.
"I go tomorrow [Saturday], so I try to feel something tomorrow [Saturday] and some Sunday," Mourinho added
"That's why I want to go there tomorrow [Saturday], not just for me, also for the boys who don't even know where the dressing room is.
"To be back there (is) a different feeling.
"I had that when I played at Stamford Bridge with Inter, but now I go to my dugout, I go to my stadium, I go to my people, so I have to control (my emotions) a little bit, because I will feel something different, for sure.
"But a couple of minutes and after that I have to be focused on the game.
"I think the fans before the match will focus on me and Roman (Abramovich, the Chelsea owner).
"Me because I'm back and Roman because he celebrates 10 years in the club and the club owes him so much.
"After two minutes they have to forget us and they have to focus on the game and the team and support the players in the team."
Mourinho is confident his team are one of six sides vying for the title in a competition he believes is collectively stronger than the one he left nearly six years ago.
He said: "I believe stronger because there is a bigger number of teams that can fight for the title, probably stronger because I think more balance, but I think a few years ago the better teams were better."