McLeish is still aiming to strengthen his squad despite having already signed eight new players this summer.
But, although acknowledging Hunt's qualities, the former Scotland boss insisted he was not uppermost in his thoughts.
He said: "It's not true. I am not about to sign anybody at the moment. We've got to count our pennies.
"I don't really want to talk about players who are with other teams or I might get into trouble with the authorities. But Hunt is a good player."
McLeish has made it clear he wants to add to his midfield department despite acquiring experienced duo Barry Ferguson and Lee Bowyer.
Meanwhile, Blues are hoping winger Keith Fahey's abductor injury, suffered in the defeat against VFB Stuttgart on Tuesday night, is not serious.
Fahey was substituted in the second half of the 2-0 reversal.
McLeish admitted: "We were going to take Keith off at half-time but thought we couldn't take everybody off and Keith is one of those who has got great energy.
"But when he flagged to the side that he had a slight abductor problem, we whipped him off right away."