The Blues are 90 minutes away from the final after they beat holders Barcelona 1-0 in the first leg of their semi-final tie at Stamford Bridge on Wednesday.
However, only the top three in the Premier League would be able to qualify for next year's campaign if Chelsea lift the trophy.
Despite the possibility of fourth-placed Spurs missing out in those circumstances, Redknapp wants to see his London rivals succeed.
"I'll be rooting for Chelsea," he said. "I haven't even thought about [missing out].
"If Chelsea stay in it, they've got a Champions League final to prepare for, and then they've got a lot on their plate haven't they? I want to see an English team win it anyway and I think they can do it."
Roberto Di Matteo's side travel to the Nou Camp for the second leg on Tuesday.