City signed centre-back Davies, 26, from arch-rivals Aston Villa in January for £2million to cover for the crocked Scott Dann. But Birmingham have lost all three games Davies has played in since joining and are second-bottom of the table.
Boss McLeish admits he may now drop the stopper this weekend when Bolton visit in the Premier League.
"I don't criticise people in public but it has been a tough baptism for him over the past few weeks," said Big Eck. "He has come in at a critical time for us when people have been missing through injury and the team have suffered adverse results.
"Whether I have to look at that, it is definitely something we have been discussing - but Curtis will be the first to know."