Manager David Moyes confirmed both Rooney and strike partner Robin van Persie will miss Saturday's Premier League encounter with Swansea at Old Trafford.
Moyes said Van Persie would still be absent for "a little while" with a long-standing thigh injury, while hoping Rooney would respond to the better temperatures.
"We have sent Wayne away on a hot weather break," said Moyes.
"His groin has not quite recovered yet.
"We have sent a fitness coach with him. He's away with the family. Hopefully we will get him fit for Chelsea."
Rooney has missed United's defeats to Swansea and Sunderland in the last week, having had a scan on his groin injury last Friday.
Van Persie has not featured since the home defeat by Newcastle on December 7, his only game since the middle of November.
"Robin is not available," said Moyes.
"He is going to be a little while. We are doing everything we can to get him back as quickly as we can."
The situation does place even more scrutiny on Moyes' work in the transfer window, although he repeated his stance that getting the right players in January is not straightforward.
"The plan and decisions won't change," he said.
"It is difficult to get targets at this time. I have said that from day one.
"I have not said we wouldn't be doing it but it is difficult."