Agbonlahor has been the subject of speculation linking him with a move to Saturday's opponents Sunderland who are managed by former Villa boss, Martin O'Neill.
But McLeish believes Agbonlahor's love affair with Villa, where he graduated through the academy, means he will stay "for the next ten years'' which would take him up to the age of 35.
The Villa manager said: "I would find it hard to believe that Gabby would leave. This is his club.
"Of course, it's football and you can never rule anything out. But I see Gabby being here for the next ten years provided he is playing at the level he is capable of.
"People here have known him longer than I have but I know how much he loves this club.''
McLeish believes Agbonlahor will be disappointed at Villa's form during the past two seasons and will be desperate to ensure they are not involved in a relegation scrap.
He said: "Gabby knows that for the last two seasons we have been in the wrong half of the table by Aston Villa's standards.
"He'll be desperate to make sure that we are okay in the next few weeks. He's a big, important factor.''
McLeish is challenging Agbonlahor to reproduce his outstanding form of the first half of the season.
He said: "That first half the season was exceptional. The evidence is there for him to look back at that and say 'look what I've done and I can produce that again'
"Gabby Agbonlahor is a match winner and he has been unlucky in recent weeks.''
McLeish has confirmed his interest in Dutch Under-21 striker Bas Dost but dismisses reports that a contact has been made with the player or his club Heerenveen.
He said: "What is the story? That he turned us down? Well, we've never approached Heerenveen for Bas Dost but we know who he is.
"We've watched a lot of the Dutch League this year but I don't know why his agent is linking us with him when we've never made any approaches or even sounded him out.
"There's been no contact whatsoever with the agent or anyone. Nothing.
"He's scored a number of goals in Holland this season but is among a number of players that we've recorded and logged.
"But you never know, he might be here in July. I'm not saying it cannot happen but we've never made any contact. We're looking at a lot of players who we believe can help us improve.''