The Tottenham boss takes his side to the Etihad Stadium in what could prove to be a crucial day in the title race, with Manchester United travelling to Arsenal later on Sunday.
City currently lead the way with a three-point cushion over the reigning champions, while Spurs are a further two adrift of Sir Alex Ferguson's men.
Mancini has been given vast funds to invest in his squad by club owner Sheikh Mansour and ended last season with the FA Cup safely banked in the trophy cabinet.
But Redknapp, who has already been embroiled in one war of words with his managerial counterpart, feels the increasing levels of expectation will only add to the weight of pressure on Mancini's shoulders.
He told the Sunday Mirror: "City are not throwing money around for fun.
"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 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."
City cruised to a 5-1 success over Spurs in the reverse fixture at White Hart Lane earlier in the season, a result which Redknapp claims helped him identify and correct certain weaknesses within his own side.
He added: "I don't like to talk about revenge. To be honest I wasn't entirely upset. What it told me was we needed to bring in a few players or we would have no chance of competing for a Champions League place.
"We had injuries, problems with Luka Modric and were three or four players short of having a team that could really challenge.
"But we went out and got Scott Parker and Emmanuel Adebayor, Modric became more settled and players came back from injury.
"Come what may I'm really proud of what we have achieved. If I had said we would be title contenders after our opening two games people would have locked me away in an institution."