O'Connor is out of contract this summer and Blues have an option to extend the deal by two years. However, it is being reported that rather than invoke that option, they will offer him revised terms.
The forward was unable to play any part in City's season beyond October because of groin and hip problems.
McLeish told the Birmingham Mail: "We have talked to Garry about an extension of his contract.
"He has been out injured a long time so we've needed to reassess things.
"But my physios in the building are saying he has been training at a very good intensity just now. They are really delighted with his progress.
"So there could be a wee bit of scope there for a contract."