Redknapp, whose side lie fifth in the Barclays Premier League standings and visit Aston Villa tomorrow, is content with his existing squad and would only look to bolster if someone 'a bit special' becomes available.
He told Sky Sports News: 'We've got so many players here it would be hard fitting anybody in.
No big spender: Harry Redknapp reckons it'll be a quiet transfer window for Tottenham
'We're not too desperate for anything. We're more than strong everywhere so unless it's someone who's a bit special I don't think we'll be doing too much.
'If someone's there that we feel can make the difference - it might just be a character or leader or somebody who can give you something at the club.
'If that type of person's available then we'd be interested, but at the moment we're not closing in on anything.'
Spurs have been linked with in-form Carroll, who has bagged 10 Premier League goals for Newcastle this season, but Redknapp does not see the in-form striker leaving St James' Park.
Hot property: Newcastle striker Andy Carroll
'He's got fantastic potential,' said the Tottenham boss.
'He's a top player, no doubt - he's a real handful and he's taken the Premier League by storm the first half of the season.
'If he was available I think there'd be plenty of people want him because he's an old-fashioned centre-forward, but I see [Newcastle manager] Alan Pardew wants to keep him and I don't blame him so I don't see him moving.'
Redknapp's attempts to move his side back into the top four over the festive period have been boosted by the news that Rafael van der Vaart is fit again after missing the last three weeks with a hamstring problem.
With games against Villa, Newcastle, Fulham and Everton coming up in the space of 11 days, Redknapp knows the festive period will be a crucial part of Spurs' season and still believes his side still have an outside chance of winning the title despite sitting in fifth position, seven points behind Manchester United.
'There are a lot of points at stake over this period and if you can get a good haul of points it makes a massive difference,' he said.
'The title race is open. Manchester United and Chelsea would be favourites, Arsenal have a big chance, and Manchester City are going to push all the way but don't write Tottenham off.'
As for Redknapp's future, he has been tipped to succeed Fabio Capello as England manager when the Italian stands down in summer 2012, but the former Portsmouth boss is not getting distracted by such talk.
'I don't think about it too much,' he said.
'I just get on with my life - that's how I am. I'm not a person who starts thinking about what's going to happen. It's 18 months down the line - you never know in this game, you never know in life. 18 months is a long way off.
Next in line: Redknapp is being tipped to replace Fabio Capello as England boss
'I love doing what I'm doing here. But I've always said if an Englishman gets offered the job it would be very hard for any English person to turn it down because it's his country.
'At the moment I'm just concentrating on trying to keep Tottenham going and getting some results over this Christmas period.
'Of course everybody wants to manage at the top level and England would be the pinnacle for anybody. But whether it would ever happen, I wouldn't be sure.'
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Explore more:People: Fabio Capello, Harry Redknapp, Andy Carroll Places: Newcastle, Fulham, United Kingdom