Redknapp's side passed a stern test of their title credentials as goals from England winger Aaron Lennon and Cameroon defender Benoit Assou-Ekotto shattered Everton's resistence at White Hart Lane on Wednesday.
Spurs have lost only one of their last 18 league games and are now level on points with second placed Manchester United and hot on City's heels.
At the start of the season Redknapp and his squad would have been more than happy to secure the top four finish that guarantees Champions League action, but now they have genuine hopes of mounting the club's first serious title challenge for over 20 years.
"The players believe we have got a chance. We have good players, a good spirit and we look solid," Redknapp said.
"(Spurs defender) William Gallas came in the other day and told the players we have got a chance.
"It's not beyond the realms of possibility. We have some real quality in the squad.
"I've been saying all along that it's not impossible to win the title. It's very hard but we have got a chance."
Redknapp is keen to keep the pressure off his players because he believes the surprising nature of Tottenham's title charge is an advantage compared to the weight of expectation at big-spending City and reigning champions United.
"The pressure is on Man City. If you look at their squad and the money they have spent on players like (Sergio) Aguero and (Samir) Nasri, they are expected to be there and win it," Redknapp said.
"Them and Man Utd are red hot favourites. We are hanging in there. The key is keeping pressure off the players. We can play with a smile on our faces.
"We have all been through times when you are struggling at the bottom and trying to nick a point to stay in the league. That is pressure."
While Redknapp is gradually starting to acknowledge Tottenham have the potential to smash the Manchester clubs' duopoly at the top, he refuses to get carried away by dreams of title glory.
Struggling Wolves will visit White Hart Lane on Saturday with the same kind of defensive tactics that characterised Everton's performance.
"I say we can win the title and then we get smashed on Saturday I look stupid. I won't put that pressure on us," said Redknapp.
"I don't look any further than Wolves. I know we are level with Man United but I'm just worried about Wolves.
"That is all I will be thinking about driving home. They will be difficult to beat. I've got to keep taking each one as it comes. I know it's a cliche but that's where we are at."
Tottenham broke through Everton's defensive wall when Lennon capitalised on poor defending by Leighton Baines to steer in the 35th minute opener and a blistering 30-yard strike from Assou-Ekotto -- his first goal since August 2009 -- sealed the points in the 63rd minute.
Everton boss Moyes has no doubts about Spurs' title credentials and he said: "Tottenham are doing well. They are title contenders and are a really good team.
"I know Everton aren't the story tonight but we played ok and had a few chances. We just needed to be clinical and we weren't."
Moyes, already without England defender Phil Jagielka, was more concerned with Sylvain Distin's fitness after the French centre-back limped off with a hamstring injury.
"He's done a hamstring, we're not sure how bad it is," he said. "I don't know if we will sign anyone. I'm going to play!"
Source: AFP
Source: AFP