The former West Ham United manager replaced Dick Advocaat at the Stadium of Light last week, with the Dutchman having struggled to get his side going following their escape from relegation last season.
Allardyce takes charge with his side sat 19th in the table, joint-bottom of the Premier League standings with Newcastle United and currently five points adrift of safety - a tough ask already.
And Redknapp says it will be tough, and he must get the best out of three experienced stars to stand a chance.
“It’s a tough job but they’re still in with a chance,” he told talkSPORT.
“He’s got a few players, Fletcher looks like he’s hit form with a few goals for Scotland and John O’Shea should be confident. He’s got Defoe who can score goals, he’s got to get the best out of these people and if he can do that, then they’ve still got a chance.”
Of the three players listed by Redknapp, Defoe is the one that Allardyce will truly be relying on to save his side.
When looking at his squad, it is clear that the England forward is the man who will be relied upon to score the bulk of goals, with the likes of Fletcher and Borini far from prolific in the Premier League.
He will first have to focus on improving a struggling defence, though, with Defoe’s goals unlikely to make much of a difference if they continue to keep conceding goals as they have done so far.