Gardner missed City's shock 1-0 home success over Chelsea last weekend with an ankle problem. But it was the recurrence of a previous injury rather than a new setback and McLeish expects him to be back available sooner rather than later.
McLeish said: "The good news is that it wasn't a fresh injury.
"It was an old injury which has changed the medical people's minds about the extent of the injury and how long he would be out.
"At first we thought it could have been a couple of months, maybe three months.
"But it is not as bad as we first thought. Craig has improved this week. He has not joined the group yet but, in the not-too-distant future, we expect him to be back training with us."