Under Mancini, the Eastlands club have spent heavily in the transfer market and risen steadily in the standings, while winning the FA Cup last season to break a trophy drought that had lasted more than three decades.
City now sit on top of the Premier League, with Spurs also chasing the title in third place - five points behind the leaders.
The two sides clash at the Etihad Stadium on Sunday, and the north London club's boss feels that his counterpart should be braced for the axe if his team do not fulfil their expectations.
"City are not throwing money around for fun," Redknapp was quoted as saying by The Sunday Mirror.
"The sheikh and the club’s supporters expect Mancini to deliver and if they don’t win the Premier League title who is to say they won’t sack him and bring in someone who can?
"Personally, I quite like Mancini and I certainly don’t blame him for spending the money he has. I would [also spend heavily] if I was in his position. But you have to accept that with it comes pressure and rising expectations.
"City have come from nowhere in recent years after living in the shadows of their neighbours Manchester United but, when you suddenly find yourself with the spending power to outbid any club, the past counts for nothing and people don’t want you to win things, they expect it."
Redknapp also admitted that if he had the financial muscle to sign players the way City have, he would have been interested in a few opposition players.
"I’d be a liar if I said I didn’t like David Silva, Sergio Aguero and Carlos Tevez," he revealed.
"They are fantastic players and with them in your side you would have to fancy your chances, wouldn’t you?"
Concerning the looming showdown, which offers Spurs the chance to avenge a 5-1 mauling by City at White Hart Lane early in the season, Redknapp added: "I’m only interested in taking three points. If we get the chance we will try and rip their throats out. We went there two years ago and had to win to secure a top four finish and came away with a 1-0 victory.
"I would settle for that.
"It’s not going to be easy but we have some very dangerous players in our side and we are more than capable of hurting them."
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