City are understood to have had an initial offer, believed to be around £2million, 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.
Charlie in the big-time: Adam (right) is excelling in the Premier League
But that will not stop McLeish maintaining his interest as he closes in on the loan signing David Bentley from Tottenham, subject to him completing a medical.
Out of favour: Blues midfielder Michel could soon be on his way out of St Andrew's to AEK Athens
McLeish also remains optimistic Rangers striker Kenny Miller will moveto St Andrew's despite reports that he has rejected the move.
The former Scotland 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.'
Meanwhile, Birmingham midfielder Michel is wanted by AEK Athens in a loan deal until the end of the season.
Michel has been unable to earn a first-team spot since his £3m move from Sporting Gijon 12 months ago.
An indication of how far down the pecking order he has slipped was youngster Jordon Mutch playing ahead of him in Saturday's FA Cup tie with Millwall after returning from a loan spell at Watford.
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Explore more:People: David Bentley, Ian Holloway, Charlie Adam, Alex McLeish Places: Birmingham, Scotland