Although Manchester United has insisted that the striker is not for sale at any price, the Chelsea manager has admitted that he only has eyes for the England man.
Manchester United has rejected two bids for the wantaway striker this summer and continues to insist that he will not be sold. Mourinho, though, publicly declared his interest in Rooney during the club's preseason tour of Asia and now says his position has not changed, despite Eto'o's suggestion that he would like to move to Stamford Bridge.
"[Eto'o] is a player with a big history in European football, but as I was saying in Asia we are trying to sign one player and we will wait to see what will happen before the transfer window closes," Mourinho told reporters. "I'm just a Chelsea manager, as every one of us [managers] is always looking to strengthen the squad.
"We all say no [we don't want to sign players] but we lie, until the last day of the market we are all waiting for something to happen, even when we say we are very happy with our squad we lie, because we always want to make it better."
Mourinho also confirmed once again that David Luiz will not be sold to Barcelona, who saw a 25 million euro bid rejected earlier in August.
"David is one of these players that the club made a huge investment in, he signed a new contract last year, he was very happy to do it, so we want to keep him," Mourinho said. "We understand that a big club like Barcelona want the best, and want to get one of the best central defenders in the world but there is no chance David is leaving."
The former Real Madrid manager also had a message for British football fans upon his return to the Premier League.
"I think I'm better than ever, because of my experience," Mourinho said. "I want to be seen like everybody else - but somebody who will give his all for his club.
"I want to say to everybody around this country at every stadium that I am one of them. I love this football country and I want to give joy to everybody."