The 34-year-old joined from Feyenoord in the summer of 2003 and his initial 2-year deal is set to expire this summer.
The Blues must therefore decide if they want to keep the tough-tackling midfielder, and the Dutch international has made his feelings perfectly clear.
"I have told the club that I would like to stay one more year. I am now waiting to see what they want to do," he told the official City website.
"They promised to tell me a yes or no within four weeks and hopefully I can stay one more year.
"Their main concern is my age, but I think I have shown that I am fit enough to do myself justice."
That assertion is backed up by the fact that Bosvelt has started all but three of City's games this season - and even then he was an unused sub.
However, 'Bosser' will be absent from Kevin Keegan's plans for the derby on Sunday as he must serve a one-game ban.