Redgrave won rowing golds at five consecutive Olympics and is the bookmakers' favourite to perform the symbolic act with double decathlon gold medal winner Thompson third favourite.
Never one to mince his words, Thompson said that athletics was a much tougher sport than rowing. The 53-year-old is a close friend of London 2012 chief and double Olympic 1,500 metres champion Sebastian Coe.
"In my opinion Sebastian Coe is the second greatest Olympian, after myself," Thompson was quoted as saying by the Daily Telegraph on Friday, responding to comments from Redgrave who said the former multi-eventer should not be considered one of Britain's greatest Olympians.
"Steve Redgrave is not in the same class as Seb Coe. He is a rower, but I think track and field is the toughest sport in the Olympics, which means the rewards are greater."
Asked whether Redgrave would be an obvious choice to light the cauldron, Thompson said: "I don't think so. It depends on your opinion."
Redgrave won the first of his golds in Los Angeles in 1984 and carried the Olympic torch during the ongoing relay while rowing on the River Thames.
Thompson will carry it next week when the torch arrives in London.
Earlier this month, Redgrave said Thompson could not be described as the best British Olympian.
"Obviously, Daley was a great athlete. Some people, Seb Coe included, think he's the best athlete ever," he told the London Evening Standard.
"My personal view is that he doesn't make the top five of great British Olympians. I'd put Seb above him, and Kelly Holmes, certainly Ben Ainslie, and, all modesty aside, myself and Matt Pinsent.
"I say that because, to me, athletes compete at the decathlon if they are great all-rounders instead of being supreme in one event."
Double Athens gold medallist Kelly Holmes is second favourite with bookmakers Ladbrokes to light the cauldron.
Former England football captain David Beckham has seen his odds tumble to 50-1 after being left out of the British Olympic team.
Organisers are keeping the decision a secret until the opening ceremony with some media reports saying an unknown youth could be chosen for the role, which Muhammad Ali famously performed at Atlanta 1996.
So who do you think should light the flame? Redgrave or Thompson? Or somebody else? Leave your thoughts below and you can also vote in our poll on the bottom right side of our Olympic page.