The Sun says he is on the Blues' hit-list of candidates to replace interim manager Rafa Benitez.
But Pellegrini, 59, has made it clear he wants to make the La Liga outfit a major force - despite the fact they have not kept up-to-date with his wages.
Pellegrini said: "I'm not looking to change club.
"My main objective is to finish my contract with Malaga and continue the work we have started.
"In the Champions League quarter-final against Dortmund I think we showed that Malaga was one of the top four teams in Europe.
"I suppose there's uncertainty about my future because nobody knows the next developments at this club yet."