The Ivory Coast international seemed to express his unhappiness at the Etihad Stadium through Twitter on Tuesday after his agent Dimitry Seluk publicly claimed his client felt underappreciated and disrespected at City.
Seluk suggested that one of Toure's main gripes was the club's failure to mark his 31st birthday last week.
But in an interview with Sky Sports News broadcast on Thursday morning, the Ukrainian claimed Toure would be more than happy to stay should he be promised a coaching position or sporting director's role beyond his retirement.
Seluk said: "Of course. Like Real Madrid did with (Zinedine) Zidane for example. Zidane played then after that he started working for the club.
"Yaya needs the club in the future.
"We don't want any more pounds, not a longer contract, nothing like this, only really attention.
"More attention (paid) to Yaya and Yaya must feel happy at the club - that's the main thing.
"I'll tell you one more time, we don't need one more pound in the contract."
Toure initially appeared to contradict claims from Seluk that he could quit the club this summer after his outspoken agent claimed City had failed to celebrate his birthday adequately.
But the player quickly backtracked and made statements in favour of his agent.
A video published by City last week in which Toure was presented with a birthday cake has since been widely circulated while many also pointed out that the club had tweeted a happy birthday message at the time.
Seluk later clarified his remarks, saying that Toure was disappointed nobody from a senior position at the club wished him happy birthday.
And on Thursday he added: "Of course some players congratulated him (on his birthday) but not the sporting director, not the general director, not the chairman, nobody.
"(The manager?) No, nobody.
"This is the question. If you don't even congratulate the player or send flowers to his wife or mother - these are just small things."