The Australian had established himself in the side for the first time with a seven-game run before suffering the setback in early December.
McLeish admits the injury is "slightly more long term" than had been originally envisaged, and said: "Chris has got the protective boot on again and it depends how it feels when he takes it off. That's going to be the key."
He added: "The last time he took it off, it was still sore. It's a ligament in his ankle. It's a kind of awkward one. If they take the boot off and he's not got any discomfort, then it could be another month."
Villa are considering loaning midfielder Fabian Delph back to Leeds after McLeish confirmed an approach had been received from the Championship club.
Delph was signed from Leeds for £6million by then Villa boss Martin O'Neill during the summer of 2009.
But he has been unable to hold down a regular first-team spot apart from a run of eight successive Premier League games at the start of this season.
McLeish said: "Fabian is one we might think about going out on loan.
"(Leeds manager) Simon Grayson did try to call me (about Delph) but I've not spoken to him yet. I think he spoke to (Villa coach) Kevin MacDonald so I'll get back in touch.
"I'm going to speak to Paul Faulkner (Villa's chief executive) to see where the club lies with it."