Blues have responded well to their 3-1 defeat at Arsenal by seeing off Sunderland before holding Manchester City at home last time out.
Birmingham are currently 14th in the table and McLeish believes his troops have every right to go to Anfield with the belief they can cause an upset.
"I think it gives players entitlement to believe in themselves," he told Sky Sports News. "They have played some good football this season.
"I don't know how the Birmingham fans feel about our overall season, but I'm sure that they have seen some pretty decent football from the team regardless of what system we've played from the first kick of the season to this very moment.
"We now face another huge challenge and the players, without Barry Ferguson, are going up to Anfield feeling good about themselves, but we know that it's a game where we're ranked as underdogs."
Liverpool 1/3, Draw 4/1, Birmingham 8/1