His last foray into management was a two-match spell in charge of the Jordan national team in March last year.
"I got fed up sitting around doing nothing. I will come and live up here until the end of the season," Redknapp told TalkSPORT on Tuesday.
"If I can keep them up then we can sit down and talk about going forward."
Former Italy international Zola resigned after a 2-0 home defeat to Burton Albion that left Birmingham three points off the relegation zone.
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They are in 20th position and play Aston Villa on Sunday.
(Reporting by Hardik Vyas in Bengaluru; editing by Sudipto Ganguly)
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