And if things go well, Alex Ferguson has dropped hints about the possibility of him featuring in the derby game against Man City this weekend.
The Japan international has been out of action since October and would be a welcome return for Fergie's squad.
The 23-year-old has scored two goals in eight appearances for United and Ferguson hopes that he will be ready to face City.
“Shinji Kagawa’s injury has been longer than we thought. He’s much better now and I don’t think he’s far away,” Ferguson told reporters.
“He started running today and he may make the bench [against Manchester City]. Obviously Nani and [Antonio] Valencia are still out and that’s why I played [Wayne] Rooney on wide right.
“I thought it was his best performance of the season. Against Cluj I’m picking a team without any thought of Manchester City. It’s a matter of who needs a game.”
Source: United Mad