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.
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