The 70-year-old was confirmed as Gianfranco Zola's successor for the remaining three games of the campaign on Tuesday, and he will be assisted in his bid to preserve their Sky Bet Championship status by former Bristol City manager Steve Cotterill.
Zola's run of only two wins from 24 fixtures has left Birmingham 20th and only three points above the relegation zone.
Redknapp's brief does not currently extend beyond ensuring safety, but if he can achieve that, next season is an enticing prospect for the former West Ham, Portsmouth and Tottenham boss.
He told Sky Sports News: "It is a challenge, it is a good club. It is three games in two weeks, massive games for us, it is a very difficult situation we are in but I am looking forward to the challenge.
"I love football, I am football mad. For sure (I could stay), keeping them up is the key to it all, we have to make sure we stay in the league next year.
"I know people criticise the owners but having met the people, they have got big plans and next year will be a big year for the club, we just have to stay in the division this year."
Redknapp will meet his new squad for the first time but will not have long to settle in as he prepares for a baptism of fire in the shape of a Second City derby at Aston Villa for his first game on Sunday.
Clashes with Huddersfield and Bristol City follow and he is hopeful of building enough confidence in his side to scrape a result along the way.
"They are very tough games," he added. "Villa away, Huddersfield, who are one of the best three teams in the division, Bristol City, who are pulling away, so they couldn't be much tougher. ]
"I am l forward to it. It is a challenge and it is something to talk about in a year or so.
"It is my first day, I will meet the lads, I haven't seen them play, I haven't got a magic wand, that's for the sure.
"The players have to get us out of it, all I can do is install a bit of confidence and belief in them and if we can do that and get a result or two then that will be great."