Chelsea head to the Nou Camp for the second leg of their semi-final with a 1-0 advantage thanks to Didier Drogba's strike at Stamford Bridge.
Barca are still favourites to progress because of their incredible home record - they have not lost at the Nou Camp since September 2010 - but Redknapp thinks the west London club stand a good chance of making the final.
Should Chelsea win the competition only three, rather than the customary four, teams will qualify for the Champions League via the Barclays Premier League.
With Spurs sitting fourth in the table, Redknapp would be forgiven for attending Tuesday's game wearing a Barca shirt and waving a huge blue and red flag in support of the defending European champions - but surprisingly, he wants Chelsea to win.
"I'll be rooting for Chelsea," Redknapp said. "I haven't even thought about [missing out if Chelsea win the competition].
"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."
At the start of 2012, Redknapp would not have been troubled in the debate about the effect Chelsea winning the Champions League would have on his team.
Back then Spurs were within touching distance of the top of the table, but now after a dramatic collapse they find themselves on the brink of dropping out of the race for Champions League.
A horrible run of one win in their last eight league games means the Londoners could be sixth in the table by the time they kick off at QPR on Saturday evening, if Newcastle beat Stoke and Chelsea overcome Arsenal.
Having kept pace with the league leaders for so long, many, including midfielder Scott Parker, believe finishing outside the top four would constitute failure for the club, but Redknapp disagrees.
"I don't think it's a failed squad whatever we do," he said.
"We're not entitled to be above Chelsea. Look at their bench the other night. They had people like (Fernando) Torres and (Daniel) Sturridge and other top players.
"I wouldn't say we've got a stronger squad than Chelsea - no way - or a stronger squad than Liverpool come to that.
"If we finish fourth we'll be delighted and if we finish third it will be even better. I can't fault the effort of the players this year whatever they do."
Parker's comments, which came after Sunday's 5-1 FA Cup semi-final thrashing against the Blues, were cutting due to the fact that he also claimed Redknapp may have started to doubt his own players after their recent dip.
The 65-year-old denied that was the case, but admitted for the first time on Friday that one or two of his players have under-performed recently.
"I don't doubt the players, I just feel that in certain positions we've just left ourselves a little bit short," Redknapp said. "One or two players have sort of tired and have not been at their best.
"I still think we will finish fourth, and third is a possibility.
"There are five games to go. Four wins will probably get us fourth but we have to think about winning all our games if we can.
"Newcastle, Arsenal and Chelsea are in the same position. It's all to play for."
Tottenham's poor run has coincided with Fabio Capello's resignation from the England manager's position, but Redknapp denies the two are linked.
Redknapp received public support for the position from within the FA for the first time on Friday, with board member Phil Gartside claiming the Tottenham manager would be an "outstanding" national head coach.
Despite Tottenham's attempts to ban questions on the England job, one reporter managed to quiz Redknapp on Gartside's comments on Friday, but he only replied: "I haven't seen anything. I haven't read any papers today [Friday]."
One topic Redknapp was more forthcoming on was the speculation about a summer bid from Barcelona for star winger Gareth Bale.
"No one has been in touch with us," Redknapp added.
"He is happy here with us at the moment. He will be linked with every club because he is such a great player."