McLeish believes the chances of it happening are "more than 50-50", but with Keane only available until the Major Soccer League restarts in March, he admitted any deal will have to be done by the start of next week for the move to go through.
McLeish said: "We are having a look at it with Robbie and trying to pursue it. That is the latest although nothing is done and dusted yet."
He added: "If we don't know by Monday, then it probably will not be done. That's why I don't want to say too much in case it doesn't happen.
"We are certainly pursuing it and at the moment, both parties are keen. I would say the chances are a bit better than 50-50."
McLeish has again insisted record signing, striker Darren Bent, is not for sale as speculation continues to link him with a move to Liverpool.
Bent, Villa chief executive Paul Faulkner and McLeish had all previously said Bent was going nowhere.
McLeish said: "We've not heard a thing from Liverpool. I'm aware of the speculation. But there has been no contact with this club and I think you've had three parties telling you that.
But, even if there was contact, we would not entertain that (selling Bent).
"We wouldn't want to entertain selling our top scorer of last season. He is a prolific marksman."
Source: PA
Source: PA