Toure scored a hat-trick in Saturday's 5-0 win over 10-man Fulham to lift City to third in the table, six points behind leaders Chelsea with three games in hand.
He said: "I came to the club to make history and I hope to continue to the end of my contract.
"I think the club and the fans need trophies, need history and need great players to come here and try to make this club great.
"We have the team, we have the players, we have the manager as well.
"I hope at the end of the season we lift this trophy for these fans who love City."
Toure's treble took his tally for the season to 20 and he attributes his fine goalscoring form to the confidence placed in his offensive ability by attack-minded manager Pellegrini.
The 30-year-old said: "He gave me more freedom up front, he gave me more confidence to attack more.
"When you play full attack you can leave some space and it is very hard because when we win it is fine, but when we lose we get some criticism by some people who think they understand football more.
"But that is part of the job, that is why we love football. We are very happy to score five goals in front of the fans and I hope we will continue to the end."