Spurs head in to Sunday's game at the Etihad Stadium five points behind the leaders, after suffering just one defeat since being thumped 5-1 by City at White Hart Lane in August.
Roberto Mancini's men are odds-on favourites to lift their first league title since 1968 and winger Adam Johnson this week admitted he would be "devastated" if the big-spending club did not win the championship.
City will move six points clear if they beat Spurs on Sunday afternoon before second-place Manchester United take on Arsenal at the Emirates Stadium, but Redknapp thinks that history dictates the Blues may struggle to hold on to their lead in the second half of the season.
"Newcastle got caught (in 1996) when they were 12 points ahead. Manchester United got caught by Arsenal that year (1998)," Redknapp said.
"It can evaporate. Nine points can go in a week.
"It's just unreal how things can change. With Newcastle it didn't do me a lot of good.
"I went to an Italian restaurant with Frank Lampard Snr on a Saturday night after we'd won with West Ham and Newcastle had gone 12 points clear with 10 games to go. And Bruno, who ran the restaurant, says: 'That Newcastle, they are a s*** team. Useless Harry, useless'.
"I said: 'I don't think so Bruno, they will win the league'. He said: 'You want a bet?'. I said: 'They're 12 points clear. You can't bet on that. It's impossible that they'll not win it.'
"He said I was afraid to bet on it and he offered me evens.
"I walked out of there like I'd won the pools but three months later I walked in and he slaughtered me. It was a big bet.
"That was the dearest night I've ever had in an Italian restaurant."
Tottenham would have gone in to Sunday's game just three points behind City had they not drawn against Wolves at White Hart Lane last weekend.
Many saw that as a sign that Spurs do not have what it takes to sustain their unlikely title assault, but Redknapp was in buoyant mood about his side's chances of victory - even though City have a 100% home record in the league this term.
Having seen Sergio Aguero, Samir Nasri and Edin Dzeko rip his team apart earlier in the season, Redknapp is all too aware of how dangerous City can be, but he insists his players are just as capable of inflicting serious damage to the home side on Sunday.
Asked if City will be scared of some of the names on Spurs' team-sheet, Redknapp said: "Of course. We have good players - Luka Modric, Scott Parker, Rafa van der Vaart, Aaron Lennon, Gareth Bale, Jermain Defoe. They're all good, attacking players.
"Kyle Walker has emerged as a fantastic player, Benoit Assou-Ekotto is a good player too.
"They are players that can carry the game to them, a bit like when we went to AC Milan and played that night when we hit them on the counter-attack."
City have lost three of their last five games in all competitions and Spurs have the advantage of taking the Blues on when they are without dynamic midfielder Yaya Toure, who is at the African Nations Cup, and their suspended captain Vincent Kompany.
"I think we can win. They are not invincible," Redknapp added.
"We lost that game in August, but we had lots of injuries and the midfield wasn't exactly what you would have expected at that time of the year, but Scott (Parker) has done well since he came here.
"My team are confident. We have good players here and they will be looking forward to it.
"I don't think about losing.
"It would be a big boost for us if we win. They haven't lost at home so it won't be an easy game. If we pull it off it will be great."