The former West Ham and Portsmouth boss is one of the out-of-work bosses whose details are being considered by the club’s Chinese owners.
The Second City club was plunged into turmoil yesterday when, after a 0-2 home defeat to fellow relegation-strugglers Burton Albion, Zola resigned.
The defeat left them just three points above the dropzone in the Championship with three matches left to play.
It brought the reign of the former Chelsea star to an end after just four-months in charge – with Brum winning just two of the 24 matches over which he presided.
Zola handed in his notice and a selection of candidates were hurriedly forwarded to the club’s Hong Kong owners.
They have been given several names to take over for the final few matches – but Redknapp is at the forefront.
Manchester City’s Under-18s boss Lee Carsley, a former player whose brother Paul is a die-hard Blues’ supporter, is another under consideration.
Also on the list is Nigel Pearson who has been out-of-work since being sacked by Derby County earlier this season.
But it is Redknapp who is uppermost in the thoughts of those recommending him to Birmingham’s board.
He has not worked as a manager since leaving the Jordanian national side but was a consultant at Derby County until the end of last season.
He has tasted success twice in the Championship, earning promotion with both QPR and Portsmouth, although his initial brief would be survival.
If chosen, Redknapp would have an interesting first outing as Birmingham’s boss – next weekend’s Second City derby at Villa Park.
What would add further fuel to the occasion is that Redknapp has a frosty relationship with Villa’s fans. A coin directed at him hit a linesman during a visit with Portsmouth nine years ago.