Tottenham beat Chelsea at Wembley to win the trophy last season but hardly managed a victory in the aftermath of that triumph, a slide that resulted in the sacking of manager Juande Ramos last month and the shock appointment of Redknapp.
Since then, Spurs have taken 10 points from a possible 12 in the Premier League to climb away from the relegation zone and thumped Dinamo Zagreb 4-0 in the UEFA Cup when born-again striker Darren Bent scored a hat-trick.
Their run includes a fortunate 2-1 defeat of Liverpool in the league and Redknapp will hope that he has not used up all his luck in a charmed start to his tenure of the London club.
"It's been a terrific couple of weeks for us," Redknapp, fast becoming a hero to the club's fans, said after Tottenham's 2-1 win at Manchester City on Sunday.
Premier League leaders Chelsea host Burnley on Wednesday, one of seven sides from outside the top flight in the last 16.
Manager Luiz Felipe Scolari will hope the competition, often belittled by the country's leading four clubs, will offer a route to his first silverware since taking the Chelsea job.
Arsenal and Manchester United are also still involved.
Arsene Wenger is likely to send out Arsenal's "kids" against Wigan Athletic on Tuesday at the Emirates, a policy the Frenchman sticks to rigidly in the competition with an impressive amount of success.
United, beaten by Arsenal on Saturday and eight points adrift in the Premier League, are at home to Championship side Queens Park Rangers on Tuesday.
Leeds United, Champions League semi-finalists in 2001, but now languishing in the third tier of English football, will try to revive some past glory when they face Championship side Derby County for a place in the last eight.
Fourth division Rotherham United, the lowest survivors in the draw, are at Premier League Stoke City while Swansea City face fellow Championship side Watford.
