The former England and Chelsea midfielder has made a strong impact at the Etihad Stadium since joining on a short-term deal from sister club New York City.
The 36-year-old's form has led to speculation that his spell at City could be extended by at least a month to February 2015.
Lampard himself says he has not given the issue much consideration but, when asked if he was tempted to stay longer, did not rule it out.
Lampard said: "The temptation is to not get ahead of myself in my career
I am here until January 1, basically, so I will focus on that and see what happens then.
"There has been a lot said about when the season starts, but the only thing that can decide my future is how well I am playing
They will be kicking me out in January if I don't play very well!
"I am just looking game to game and trying to play as well as I can."
Lampard signed for New York, who enter Major League Soccer in 2015, after being released by Chelsea at the end of last season.
The opportunity subsequently arose for a short-term spell at City to maintain fitness ahead of the next season in the United States.
He was not considered by manager Manuel Pellegrini for selection in the opening weeks of the season due to a lack of match-sharpness but he has made up for it since.
Lampard has delivered a series of influential displays in the past three weeks and scored four goals, including a vital equaliser against former club Chelsea.
Lampard, asked about how the fans have taken him to heart, said: "I have scored a few goals and I hope they can see my desire
I haven't come here just to train and make up numbers in the squad.
"People might have thought that was the case but it's not
I want to perform - I have always done it throughout my career, and if people see that I am giving my all the fans will get behind me."
Source : PA
Source: PA