The summer signing from Aston Villa has been out of action since the pre-Christmas win at Fulham and Sir Alex did not expect him back for around four weeks when addressing the media on 8 January.
"It's going well," he admitted at the Betfair presents Man Utd live webcast at Old Trafford on Thursday. "I've been in the gym most days but it's getting there and hopefully I'll be back soon.
The England international admits he is loving life in Manchester after moving from the Midlands to link up with the champions and feels his own game has developed over the past six months or so.
"I'm enjoying it," he added. "From the minute I stepped into the building, I was welcomed with open arms by everybody in the squad. All the staff have been brilliant and to play alongside so many world-class players was always a dream for me.
"It brings your game on and you go up to another level. You experience that straight away. There's competition for places all around the team so you've always got to be on your toes.
"I think my game has come on," he admitted. "I've added different things to my game. Obviously, we're playing a different style than it was at Aston Villa and I've had to adapt.
"When I've gone away with England and the likes of Wayne Rooney and Michael Carrick, I've got to know the boys there and how they play. Straight away, I had a good pre-season under my belt and have been going out and wanting to do well."