The Italian has come under increased pressure after allowing the gap between themselves and rivals Manchester United at the top of the Premier League table grow to 12 points.
With the club also exiting the Champions League earlier in the season, speculation has seen a number of high-profile managers linked with taking over at the Etihad Stadium in the summer.
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When asked about Pellegrini being linked with his job, the 48-year-old replied to reporters: "F****** hell! I can't continue to answer questions about this every week.
"We have another two months [of the season]. You know things can happen in that time.
"But this is normal for you [reporters]. This is your job, don't worry. But I can't continue to answer every week about one name or another.
"Also because I don't understand the reason for this. Why would Manchester City change their manager? For which reason?
"In the last 18-20 months, after United won the Premier League in 2011 and we won the FA Cup, there were seven trophies available to win.
"Manchester City won three of those seven. So I don't understand [why City would change their manager]. For what reason?
"I am not the CEO or chairman, so if you want to ask these questions, you should speak with them. I don't have a problem. I have another four years on my contract and we are doing well."