The 'Vital Villa' fans' website posted a message earlier this week calling on supporters to voice their feelings an hour before the meeting with the current Barclays Premier League leaders.
But McLeish has thanked the majority of fans for their backing of his players in what he admits was always going to be a season of transition with Villa hovering around midtable. He said: "I know there were a few Villa fans at the start of the season expressed dissent at me becoming a manager."
He added: "That is out of my control but I know the silent majority of Villa fans have been absolutely tremendous in supporting the team home and away.
"I've met some of the fans and I really felt their passion but I think they felt mine as well - and I'm determined I'll get it right at this club.
"I do believe in one or two other seasons there have been sticky moments as well. This season is a bit of a rollercoaster but the points are there for us to climb the table."
As regards the intended protest, McLeish said: "It is out of my control, it is a modern day fashion.
"There were rumours of a protest against Arsene Wenger a couple of weeks ago so I'm in pretty good company!
"At the same time, it's not something I'm going to say I enjoy because we all like to be popular.
"It's a minority and something out of my control. But the one thing I can control is the team and what effort they put in to get the best out of them because I am pretty good at that."