The 59-year-old's reputation has been boosted by an impressive spell at the helm of Malaga, who he this season led to the Champions League quarter-finals despite off-field distractions.
Pellegrini managed Villarreal and Real Madrid before that and there are suggestions his next destination could be Stamford Bridge.
Reports say a meeting took place last week between Chelsea and Pellegrini's representative, which has led bookmakers to shorten their odds on him becoming next manager to as low as 2/1.
Pellegrini still remains second favourite for the job, though, with Jose Mourinho the overriding favourite.
The Portuguese is expected to leave Real Madrid at the end of the season and has long been linked with a return to Stamford Bridge, where interim boss Rafael Benitez is under contract until May.
Mourinho would undoubtedly be the fans' choice, having steered Chelsea to two Barclays Premier League titles, an FA Cup and two League Cups during three years in west London up until September 2007.
Chelsea chairman Bruce Buck was last week asked if anyone had been ruled out and about Mourinho in particular, to which he responded: "I am completely open minded about it."
Speaking to Al Jazeera, Buck added: "We really haven't started that [search for a manager] yet. We're all thinking about it and have some ideas and certainly Mr Abramovich is thinking about it.
"At the moment we're concentrating on the end of the season."
Source: PA
Source: PA