Villa have had a largely inconsistent season and with eight games remaining they find themselves a mere five points off the drop zone.
With the likes of Liverpool, Manchester United and Tottenham all lined up McLeish’s side face a daunting set of fixtures for their run-in, though the manager remains positive he will avoid another demotion.
"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,” McLeish told reporters.
"It will maybe be on the tip of everyone's tongue. It is not something I believe will happen.
"I'm sure the players will think about it as well, as they are only human. They were in a battle last season, so they've been through it, and they've got to do it again this season.
"Every week will be a battle but we are only three points off West Brom, and have a game in hand."
When at full strength, Villa boast a squad brimming with internationals and would have been hoping for a top-half finish as a minimum aim for this season.
However, McLeish insists he faced a much tougher proposition than his predecessor Gerard Houllier after having to cope with injuries to a number of key players.
"I never thought it was going to be easy this season. We have a lighter squad than Villa had this time last season,” he continued.
"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."