Rooney continues to be linked with a move away from Manchester United despite the club saying he is not for sale.
When asked if he might be interested in signing Rooney, Mourinho said: "It’s a tricky question because from an ethical point of view I can’t talk about players from other teams.
"You know me, it’s not my type of character to talk with a bit of hypocrisy, but he’s a player I like very, very much. I can’t say more than that without being fast and direct but he’s a Manchester United player."
Chelsea and United are both in Thailand at the moment as they prepare for pre-season friendlies.
However, Rooney has already flown home after scans revealed he had torn his hamstring.
While new manager David Moyes has expressed his desire to keep Rooney at Old Trafford, Rooney himself has remained quiet on his future.
Rooney did, however, speak about his injury.
"Gutted to have picked up a niggling injury especially as training was going so well, heading back to Manchester to have it assessed fully but early indications are nothing to worry about," he said on Facebook.
Moyes admitted he was sad that Rooney had to fly home.
"It’s disappointing, The day we left he just felt his hamstring tighten up right at the end of training and we thought there would be no problem," he told MUTV.
"But after the long flight we decided we’d get him tested and scanned and have a look at things and there is just a small grade one injury there.
"He didn’t train yesterday and we thought it would be worth just seeing what it was and there was a very slight mark on his hamstring. We won’t take any chances - there is no point in taking him any further round the world so we’ve sent him back and he’ll get treatment at the Aon Training Complex."
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