Mourinho hinted yesterday after Chelsea beat Hull City 2-0 in the opening game of the season that he would likely pursue Rooney until the end of the window.
United have so far rejected two bids from the west London club, insisting the England international is not for sale, and as the Premier League champions defeated Swansea 4-1 on Saturday Carrick insisted that Rooney was an integral part of the win.
"I thought he came on and looked good," Carrick said of Rooney's substitution in the 62nd minute of the match.
"He set up two goals and that's what he's all about. He's a real threat. He got a bit of a whack [on his Achilles] when he made Danny's second but I'm sure he'll be all right. He's a big Manchester United player. He's one of us and we all stick together.
"When we're on the pitch we fight for each other and do what we can for Wayne. He's certainly part of that."
The United fans were equally supportive of Rooney over the course of the match, looking to have forgiven the striker who is believed to have handed in a second transfer request in three years just before the end of last season.
Carrick said of the supporters: "He's given this club an awful lot so the fans support him and we support him. As I said, we stick together. It was a good day."
Rooney's future will certainly take the forefront as United prepare to face Chelsea this weekend, and Mourinho has been anything but candid in his public adoration of the striker in recent weeks.
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