Redknapp took charge at St Andrew’s with three games remaining last term and the 70-year-old was able to preserve their Championship status with victories in the final two matches.
But, after their home defeat to Preston North End made it six consecutive losses in all competitions, it was announced that Redknapp would not be seeing out the one-year contract he signed in the summer.
Former Blues midfielder Lee Carsley has been placed in caretaker charge of the club, who currently sit 23rd in the Championship table after their first eight league games, above only promoted Bolton Wanderers.
Birmingham signed 14 players during the summer transfer window but a failure to stop the rot saw Redknapp become the first managerial casualty of the Championship season.
Grimsby are open to talking to Sol Campbell about their vacant managerial position.