The Blues have seen two bids for the England international rejected by the Premier League champions - with their most recent offer thought to total £30 million with add-ons - with the forward understood to fear a backlash from the fans if the club force him to stay at Old Trafford.
| MANCHESTER UNITED LATEST
|14/1||Wanye Rooney is 14/1 with bet365 to be Premier League top scorer this season
"There is no time limit on it," Mourinho is quoted as saying by the Daily Mail.
"We have identified the player as one we would like to have with us. We have done it in an ethical way and we are going to do that until the last day. We are doing things legally, making the official bid directly to the club."
Mourinho, though, insists no Chelsea official has spoken to Rooney regarding a move to Stamford Bridge without the consent of United but is hopeful of entering negotiations before the end of the transfer window.
"There have been no direct relations with the player, no contact - absolutely nothing. So let's see if things change."