City's Greek striker is aware of Blues' interest and is said to be mulling over a possible move to St Andrew's, according to sources in the north west, says the Birmingham Mail.
City are likely to accept a fee in the region of £2.5million for the 22-year-old.
There is a feeling Samaras needs regular football to rediscover his form and confidence.
In 36 starts for Manchester City, he has been substituted 29 times and under Stuart Pearce's management he was used mainly on the left.
McLeish will have checked out his character thoroughly and been told Samaras is a good professional and a likeable person who is no trouble off the field.