The 59-year-old Chilean coach has been sounded out by the European champions as the man to replace interim manager Rafa Benitez when his seven-month contract expires at the end of the season.
According to reports in Spain, Roman Abramovich is keen to bring Pellegrini to Stamford Bridge, but is holding back from making a formal offer for his services until Chelsea have guaranteed Champions League qualification.
The South American tactician guided Malaga to the quarter-finals of Europe's elite club competition this year, despite continuing financial problems at the Spanish club.
Renowned as a disciplinarian who has successfully implemented a brand of attractive, attacking football, Pellegrini's pedigree is unquestionable, and he can count himself unlucky to have been eliminated by Borussia Dortmund earlier this month.
He might get another stab at the Champions League with Chelsea next term, though, as the Blues reclaimed third spot in the Premier League table last night, after a comfortable 3-0 victory over Fulham at Craven Cottage.
Two goals from John Terry, and a David Luiz thunderbolt, settled the west London derby, putting them back on course for a top-four finish in 2012/13.