Jenas has managed to recover from successive injuries and is looking to complete a full week of training ahead of the clash with Norwich on Saturday.
“I thought it was a little bit early for Jermaine last weekend at Sunderland,” McLeish told the club’s official website.
“I said to him it was good for him to get a good week behind him and then we can consider introducing him into the squad for the Norwich game.
“He trained on Monday and did a separate bit away from the group on Tuesday because of the intensity of our session.
“He’ll work on Wednesday and then Thursday and Friday he’ll be back with the group.
“I know the fans are keen to see him and I am keen to see him aswell. We want to get him into the action as quickly as we can.
“I’m confident that we can get him involved with the squad this weekend.
“It’s all about match fitness but we’ve not really got a chance to give him a lot of match practice before plunging him right in.
“We’ll see whether he’s ready to be in the 18 this weekend, but the signs are very good.
“Obviously it gives me a selection problem with players getting left out and that will be the hardest thing.”