Tevez has fallen out of favour with City boss Roberto Mancini after a series of high profile spats caused the Italian to transfer list his former captain earlier this season.
Despite claims that Tevez is close to a transfer to AC Milan, it has been suggested that Redknapp is keen on offering the 27-year-old a chance to stay in the Barclays Premier League with a move to White Hart Lane.
Redknapp has repeatedly stated his desire to land a marquee signing in January that he thinks will boost his team's title push, but admits signing Tevez would be a risk not worth taking due to the Argentinian's wage demands.
Tevez is reported to be on £250,000 a week at the Etihad Stadium - around four times what Spurs offer their top earners.
"I like him. He is a great player," Redknapp said.
"He is fantastic. A battler, a real talent but we are not going to be able to get him.
"It's not happening. We are not pursuing it.
"The chairman won't put the club in trouble for one player. His wages would be astronomical."
Tottenham started the season with heavy defeats to the two Manchester sides but have lost just one game since and they now face a crucial month in which they can cement their status as serious title challengers if they maintain their current form.
Ledley King has played a major part in turning Spurs' fortunes around.
King played just nine games last term but he has already turned out 11 times this season and Spurs have not lost a game when the defender has played since August 2010.
There were worries that this year could be the centre-back's last at the club when Redknapp claimed that he would only be offered a new deal if he completed 20 games.
He backtracked on that idea, however, insisting that there is no chance of King leaving the club when his current deal expires at the end of the season.
"He's part of the furniture, he's a big part of this football club and I'm sure the chairman knows that as well," Redknapp said.
"I'm sure he will look after him, I don't see Ledley leaving here, he hasn't got to play 20 games.
"If he plays 12, 14 or 16 games, I don't think anyone's going to go: 'well you didn't reach 20'.
"There's enough goodwill towards Ledley here for what he's been through and what he is.
"If he only plays 10 games the chances are you might win the 10."
King's chronic knee problem means he will not play at Swansea on Saturday, but he is likely to be available for Spurs' following game against West Brom on Tuesday.
There was good news from the treatment room regarding Michael Dawson.
The former Nottingham Forest defender has missed the last four months with an Achilles injury, but is now back in training and has been pencilled in for a return in next month's FA Cup third round game against Cheltenham.
Redknapp is delighted to have the defender back and now hopes he can put in a string of performances to work his way in to England's Euro 2012 squad.
The Spurs boss said: "He can get in the squad. Hopefully he will. I'd love to see him go, he went to the World Cup.
"It's great to see Michael back, he's a great guy, a great player and a great pro."
Jermain Defoe is in contention for a place in Tottenham's starting line-up after making good progress in his recovery from a hamstring injury, but Redknapp may stick with the same XI that beat Norwich 2-0 on Tuesday.