With only goal difference separating the two sides, Redknapp's Tottenham could help City end this weekend above
United by denying them all three points at Old Trafford on Saturday night.
That would also help Spurs' hopes of finishing in the top four of the Premier League, with the visitors just two points further back.
Redknapp believes City are only going to get better if they continue to splash the cash, but is confident United have enough to fend them off this season.
Asked if City were set to overtake United, Redknapp said: "They're going to push them all the way, obviously.
"They're going to keep improving but, at the moment, I still wouldn't want to bet on Man City finishing in front of Man United this year.
"If you asked me to put my life on it, I think I'd still go with Man United."
Redknapp believes even if City do eventually eclipse United, it will be for one reason.
He said: "The chairman (Daniel Levy) said to me once, 'How come Chelsea, Arsenal, Man United, Liverpool, or whoever, win the league every year?'
"If Ian Holloway had £150million-£200million to spend, he'd be close to winning the league at Blackpool, wouldn't he?"
As well as City improving, there has been talk of a decline at United, but Redknapp cannot see them getting significantly weaker while Sir Alex Ferguson remains manager.
"Man United will still produce players there, and they'll still be there, as long as Alex is there as well," he said.
"You've got a special manager there who won't take being second best."
The rise of City, who Spurs narrowly beat to fourth spot last season, is also bad news for Spurs.
"Man City are the one team who are maybe a bit stronger than they were last season," Redknapp said.
"I think Arsenal will be in the top four. They are looking good.
"I still wouldn't write Liverpool off and Everton will be pushing. So it's going to be hard but we have got as good as chance as anyone."
Ending their 17-year winless run at the homes of the so-called big four would certainly help Spurs' cause.
They have not won at Old Trafford for even longer, almost 21 years in fact.
Redknapp said: "Our league position is really the key because we need to finish in that top four if we want to be in the Champions League again.
"It's important that we keep trying to pick up league points, even though we're going to a great stadium with a special atmosphere and great tradition.
"It's always a massive game and hopefully we will go up there tomorrow and perform."