Reports suggest that Carter was set for a loan move to Rotherham but the deal as been put on hold because of injuries and suspensions to a number of Blues midfield players.
Millers boss Ronnie Moore has been a long-time admirer of the England Under-20 international having tried to take him on loan at the same time last season.
Carter has not been an automatic choice in Steve Bruce's first team squad this season but with Damien Johnson suspended for the game against Leicester this weekend, Stan Lazaridis returning for his first game after a month out with a hamstring injury, David Dunn a long-term injury casualty and Stephen Clemence struggling with shin splints, Blues are reluctant to let Carter move to Millmoor at this time.