The 31-year-old, who still has three years left to run on his current deal, initially used Twitter to distance himself from comments made by his agent Dimitry Seluk but then reversed his position in a television interview.
Nevertheless, Redknapp says the Ivory Coast international is likely to remain at the Etihad Stadium next year amid rumours of a return to Barcelona, whom Toure left to join City in 2010.
"I'll be amazed if he's not a Man City player at the start of next season," Redknapp told Sky Sports News.
"These things are normally an agent angling for a new contract and maybe he looks at other players - across the road Wayne Rooney's getting £300,000 a week, so they say - and may think 'well, that's what I should be on'.
"I thought I'd heard it all, but this (the complaint about Toure's birthday celebrations) is a new one to me. I was at the Etihad for the last game of the season and the reception he got when they called out his name to go and get his medal was the biggest, they absolutely idolise him there.
"The fans love him and he's been a revelation in the Premier League this season with 20-odd goals from midfield. But sometimes these things don't always have a happy ending."
Meanwhile, Le Tissier, who played his whole professional career at Southampton, says City should take a strong stance over the situation.
"It's that bizarre I find it difficult to believe it's actually true but the world has changed since I played football," he said. "I don't remember people being that precious back in my day.
"But I would have thought he would be at Man City next season. If I was the Man City hierarchy, I'd insist that he was. If he's not that happy then I don't think it's a problem for them to put him in the reserves or with the kids and just say 'look, if you're not happy, just sit there for a bit and we'll get someone else in'."
Redknapp added that, ironically, Toure's age could be a factor in how the situation resolves itself.
"He was voted the player that Barcelona fans would most like to see back at the Nou Camp," he said.
"Man City have to be clever and they have to be commercial as well. You've got a 31-year-old, what are you going to give him, another four-year contract?
"Giving players four-year contracts at 31 is a dangerous game to get into. If you look at what Chelsea are doing, when their players are getting to 31, 32 they're only getting one-year contracts. I can understand Man City's position and they've got to be strong."
And Sky Sports Spanish football expert Guillem Balague says Toure should adopt a different approach if he is looking to engineer a move away from City, claiming 'we have seen it all before from him'.
"He is using the same words as he did at Barcelona, but he should change his tune if he is going to try what he is trying to do which is a contractual situation.
"Now everyone knows he is upset, I say upset in inverted commas. He is available or if you (City) want to keep him happy just give him another contract. That's what it is all about.
"The birthday scenario was nothing. It started the whole havoc based on nothing but it is one way of starting what it is really... a contractual situation.
"It happened at Barcelona two years after he arrived there. All in all it is just a strategy which has just given us something to talk about for the rest of the summer."