Blues are understood to have had an initial offer, believed to be around £2 million, rejected for playmaker Adam.
Blackpool boss Ian Holloway has already indicated he would be surprised if any of his players wanted to leave this month unless one of the leading clubs expressed an interest.
But that will not stop McLeish maintaining his interest as he closes in on the loan signing of David Bentley from Tottenham, subject to him completing a medical.
McLeish also remains optimistic Rangers striker Kenny Miller will move to St Andrew's despite reports that he has rejected the move.
The Blues boss said: "We are delighted David has chose us because there were half a dozen other clubs interested and he is a quality player.
"As for Kenny, he's not said yes or no. He's not knocked us back as some reports have suggested. Let's wait and see."