Young has been sidelined since United's pre-Christmas win at Fulham and was only expected to make his return in the first week of February.
However, Young could be fit for United's game with Stoke on January 31st although the former Aston Villa man will definitely miss Sunday's high profile clash with Arsenal.
"It's going well," he said at a 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.
"It's going to be a tough game [against Arsenal].
"But I'm sure we'll go down there full of confidence and looking to get three points - as we do in any game.
"There's a lot of points to play for and everyone wants to be top of the table but there's plenty of games left and we've got to concentrate on ourselves and look to go down there and win."
Young scored a brace in United's now famous 8-2 win over the Gunners the last time the two teams met and the England international admits he is thoroughly enjoying his time at Old Trafford since arriving in the summer.
"I'm enjoying it," he said.
"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 added.
"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."
United currently sit second in the Premier League and travel to Arsenal on Sunday.