Chile winger Jean Beausejour, Czech Republic defender Martin Jiranek and Belarus midfielder Alexander Hleb joined Blues on a busy transfer deadline day, prompting talk the club could improve on last season's ninth-place finish.
However, McLeish does not want fans to get carried away and insists he will be content first and foremost just to stay in the Barclays Premier League.
"That's nonsense to start talking about that," the Blues boss said.
"I thought silly season finished when the window closed.
"I don't think we should be thinking about that. We're still a fledgling Premier League team. We want to establish ourselves and develop again.
"If we finish in the top 17, like the targets I set last season, then I'll be happy."
Source: PA
Source: PA