Toure's agent claimed earlier this week that his client was looking for a new challenge after winning both the FA Cup and Premier League with the Citizens.
However, Mancini has claimed that everyone at City shares Toure's desire to keep progressing and add more silverware to the Etihad Stadium trophy cabinet.
The Italian said: "Every day we have a new challenge here. In two-and-a-half years we won the FA Cup, the Premier League, the Community Shield.
"Now we need to win other cups and other Premier Leagues. We need to work more for this challenge. I think Yaya thinks like me and the other players.
"I am happy Yaya wants a new challenge, I also want a new challenge. I want to win the next game, then the next game in the Champions League. We want to do everything together."
Toure has been linked with a return to Barcelona, whom he left to join City in a £24m move in 2010.