Redknapp: Tottenham not getting carried away
"We are not getting carried away," he told a news conference ahead of the visit of Wolverhampton Wanderers on Saturday. "I am certainly not anyway. As I said at the start of the year, we are looking to try and get back in the Champions League this year.
"It is going to be difficult because the top six are all good sides. They have all improved and it is going to be very tight. I still see it being that way. But we are in a good position at the moment."
A win over Wolves - which would be their ninth in their last 10 home league games since they lost 5-1 to City in the second game of the season - would put Tottenham level with Roberto Mancini's pacesetters who visit Wigan Athletic on Monday.
Spurs are the form team having won 14 of their last 18 Premier League outings after thrashings by United, who beat them 3-0 at Old Trafford, and City in their first two league games of the season but Redknapp is cautious about their title chances.
"It is going to be difficult, very difficult. We are certainly not the favourites. To finish above Manchester United will be in our wildest dreams. I never thought I'd be thinking about that. It is going to be difficult, let's see how it goes."
Redknapp also ruled out bringing any marquee signings to the club in the January transfer window because of the cost.
"We can't quite buy those players," he said. "We are not in a position to go and pay 40 million pounds and 200,000 pounds a week [on wages].
"The chairman [Daniel Levy] doesn't run the club this way and quite rightly so. We get 36,000 people [in the ground], we sell out every week [but] we are not in a position to do that.
"That is where we are, and I am very fortunate. A lot more fortunate than most of the managers in the league.
"There are lads who are working with shoestring budgets and doing the best that they can. I am one of the fortunate ones really, just short of having the kind of money the top three of four have.
"They have got more spending power than we have, there is an awful lot below who don't have anywhere near like the spending power we have."
While a big-name signing may not be on the horizon, Redknapp is also reluctant to let anyone go despite the likes of South Africa international Steven Pienaar being the subject of a bid from Queens Park Rangers according to British media.
"I wouldn't want to let him [Pienaar] go. He is a good player," he said. "Really, I don't have any need to weaken the squad.
"I would rather have a good squad around me for these last 18 games [of the Premier league season], rather than letting one or two go who could play a part for me because you never know when you can run into injuries."