Kim signed for the promotion-chasing championship side in the final moments of January and has already impressed the former Manchester United player in training.
"He trained for a couple of days and he was really good on the ball - technically a very good player," Greening told the Birmingham Mail.
"That's what the gaffer looks for first and he is technically good on the ball and can pass with both feet. He was only here for two days so it will be nice to see him over the course of the week and then in a game situation.
"His pedigree is good and he has played for his country so he must be a good player," he said.
"You want competition. The more players we get and the more competition we have, the better it is for the whole squad."