But he has "not closed the door" on LA Galaxy striker Edson Bubble, who has returned home after training with Blues for the past week.
Carew, Villa's leading scorer for the past three seasons, has struggled to make an impression during the first half of the campaign. He was also involved in a public fall-out with Villa manager Gerard Houllier.
But McLeish is cool on the idea of signing the Norway international - out of contract in the summer - should he become available in January.
He said: "I have always liked John Carew as a player and I tried to take him to Rangers. But he is not someone I have thought about."
As regards Buddle, McLeish said: "He has gone back and we will keep the door open. We are not in the position to make any offers at the moment because we are looking to try and bring a more experienced player into the club. We've not closed the door. He did okay."
Source: PA
Source: PA