McLeish went down as Birmingham boss last May, with Wolves pushing them into the bottom three on the final day of the campaign, and now Villa find themselves only five points above the drop zone and with eight senior players sidelined.
Asked about the prospect of back-to-back relegations, McLeish said: "I don't believe it will happen. That is my school of thought. I know the media will bring it up, that's fine, I can handle that. It will maybe be on the tip of everyone's tongue. It is not something I believe will happen."
He admitted the campaign run-in will be tough, saying: "Every week will be a battle but we are only three points off West Brom, and have a game in hand."
And he said he had expected this season to be a testing time in what he has stressed is a transitional period for the club.
"I never thought it was going to be easy this season. We have a lighter squad than Villa had this time last season. I knew from that point of view it was going to be a big challenge again.
"But I'm confident the players can rise to the challenge and make sure we are okay this season."
McLeish has revealed his determination to show leadership to his players while coping with the setbacks suffered by Fabrice Muamba and Stiliyan Petrov in recent weeks.
Bolton midfielder Muamba, who played under McLeish at Birmingham, suffered a cardiac arrest last month but is making a good recovery, while Villa skipper Petrov has been diagnosed with acute leukaemia.
The Scot said: "You have to show that you still have the focus, the passion, everything that goes with concentrating on the game itself. You get these traumatic times in life and you have to deal with them. You move forward and show leadership and get everybody playing to the best of their ability and believing in themselves."
Source: PA
Source: PA