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.
Source: PA
Source: PA