Carrick pulled out of England's squad for the double-header against Slovenia and Scotland after suffering a groin injury in training.
The 33-year-old will start his rehabilitation at Carrington later this week and United boss Louis van Gaal will aim to have Carrick fully fit by the time his team take on Arsenal a week on Sunday.
Carrick has only played twice for Van Gaal because of an ankle injury he suffered just before the Dutchman took over.
But he is more than happy with life under the former Ajax coach and he is keen to extend his contract, which expires next summer.
"My contract is up at the end of the season. I want to stay, of course. I've got nowhere else to go." said Carrick, who has been at Old Trafford for eight years.
Carrick confirmed talks over a new deal with United have yet to begin, but the former Tottenham Hotspur midfielder is not concerned.
"They have not really, not yet," Carrick said regarding the beginning of discussions. "But I haven't expected (that) to be honest, with the injury. It will probably around Christmas or after that."
Carrick suffered an ankle injury just before Van Gaal flew into Manchester after guiding Netherlands to third place in the World Cup, but he has been impressed with the new coaching staff.
"It was literally his first day in the office when I went for my operation, so that was shocking timing really," said Carrick.
"But he was great with me straight away, the boss. He has been great, and his staff. They have been really supportive from the first day and I have a lot to thank them for because he had a lot on his plate coming in.
"He took his time to make sure I was all right and getting on the right track."