The 25-year-old righdefender's current loan deal will expire this weekend but the Blues boss wants to extend the deal so that he has cover in the right back area.
"We're in the process of trying to extend it for another month," McLeish told the Birmingham Mail.
Hunt picked up a hamstring strain in the away draw against Wolves last weekend but has recovered in time to play in the match against Watford at St Andrews on Saturday.