Camoranesi, available on a free transfer, has already held talks with City about a move to St Andrew's and the 2006 World Cup winner has created a favourable impression with McLeish.
But the former Scotland boss has to be convinced Camoranesi can still make a telling impact at the age of 33 before giving the thumbs-up to the deal.
Camoranesi's Juventus team-mate, 32-year-old defender Fabio Grosso, also remains a target for McLeish.
But the Italian giants are looking for a fee while Birmingham would prefer to sign him on a free transfer even though he has two years remaining of his contract.
Meanwhile, City remain among the front-runners to sign AK Alkmaar striker Moussa Dembele in a £5million deal after holding further discussions.