Reports suggested in midweek that the former Barcelona man was hungry for another challenge having won the Premier League and FA Cup with the Blues.
Interest would be high across Europe for a player regarded as one of City's finest.
However, Mancini has insisted Toure is happy at City and is delighted he wants more challenges as there are plenty to be had at the club every day.
The Italian manager believes Toure should use the chase for Champions League glory with the Premier League champions to spur him on.
Mancini also believes that defending the Premier League title is another huge challenge in itself that Toure can chase if he is feeling the need for more tests.
"Every day we have a new challenge here because in two years we won the Cup, Premier League and the Charity Shield, now we need to win the other cup," said Mancini.
"In the Premier League, we need to work more for this and this challenge (of defending it).
"I am happy that Yaya wants a new challenge, I want a new challenge, I want to win the next game, I want to win the Champions League. I have no concerns."
Mancini's side face West Brom on Saturday and he insisted his players will wear the "Let's Kick It Out" racism t-shirts despite some pleas for black players to avoid wearing them after recent cases.
"We are all against all forms of racism," said Mancini. "The world is different, there are some people different from us. We need to work together to improve this situations. Yes they will (wear the t-shirts).
"I think we can do more what we do in this moment but sometimes stupid things happen, when you're on the pitch you say things you don't think."
Mancini will be focused on the game, however, and is hoping the international break does not scupper his side's return to form.
City won their last game before the break with a convincing victory against Sunderland but the Italian manager admits it can be tough to come back after the break.
The postponement of England's game with Poland in Warsaw from Tuesday to Wednesday has also hindered some players while David Silva picked up a hamstring injury playing for Spain.
He said: "When we come after the international break, the game is very difficult. Today is the first day we can work together.
"We have a lot of injury problems, David has a hamstring problem and will not be ready for tomorrow. English players who played on Wednesday are tired.
"We hope that maybe the next league game against Swansea, David will be ready. The England players are not a worry but because they played on Wednesday they are tired. I am not worried, they have another day to recover. That is a situation that can happen."
Source: AFP
Source: AFP