Spurs are currently third in the Premier League after an excellent run of one defeat in 17 matches left them just six points off leaders Manchester City at the half way stage.
They started 2012 as the capital's top club for the first time in 17 years after opening up a five-point gap on Chelsea that will increase further if they win their game in hand against Everton on Wednesday.
Redknapp concedes, however, that Spurs are fighting a losing battle against Chelsea off the field, due to the financial clout of their west London rivals.
Luka Modric's head was turned by Chelsea's offer to treble his wages last summer and the Blues look set to pip Spurs to the signature of Redknapp's long-term target Cahill - a source of huge frustration for the Spurs boss.
"It's difficult trying to beat Chelsea if you're going for the same player, because their wage structure would be on a different level to ours," Redknapp said.
"If you're in for the same player, they'll blow you out of the water.
"I like Cahill, he's a good player. But if you make him offer, then Chelsea can give him more. You can't really compete in terms of making him an offer.
"That's the problem. You are competing, trying to finish above them, but it's not easy."
Tottenham's title tilt may be hindered in the second half of the season by a number of injuries. Redknapp confirmed this morning that Sandro and William Gallas both suffered calf tears in Tuesday's 1-0 win over West Brom, and the Spurs boss is already without Scott Parker, who is struggling to overcome a knee injury.
That has left him with two fit central midfielders - Luka Modric and Jake Livermore - while he is also short in numbers in defence, with Younes Kaboul, Sebastien Bassong and Michael Dawson his only fit centre backs.
Redknapp recently played down suggestions he would be active in the January transfer window, but he now concedes his current injury situation may force him in to the market.
"Injuries are a problem," Redknapp added. "Parker, Sandro, and Modric looked great as a three in midfield, but then I suddenly lost my two powerhouse players and it doesn't quite look the same. It's something we have to look at really. We are short there and in defence.
"Sandro and Gallas both have calf tears. I don't know how long they will be out for.
"I'm hoping that Ledley King can continue playing when he can and Michael Dawson is coming back from an Achilles (problem) that he has dragged on for two years.
"I only really have Younes Kaboul and Sebastien Bassong, who is looking to leave, so I am not over-loaded.
"It will be the team with the strongest squad who will win the league. We have a strong squad, but in one or two positions we haven't got a lot of cover. It's a problem and the chairman and I have spoken about one or two players."
Redknapp denied making an approach for Junior Hoilett and Christopher Samba, but hinted that a move for the Blackburn duo is possible.
"I'm sure (Rovers boss) Steve Kean will want to hang on to them in their situation, but they are good players," Redknapp said.
Redknapp denied reports he has already made a move for Santos midfielder Ganso, however.
"I've never heard of him," said the bemused Spurs boss.
Redknapp will rest the majority of his first team on Saturday for Tottenham's FA Cup third-round game against League Two side Cheltenham.
The Spurs boss denies fielding a weakened team means he is not taking the competition seriously, however.
"I will make lots of changes but the team will be full of almost all international players," Redknapp said.
"It's a competition we want to win and we have as good a chance as anyone do it."
