The Hammers confirmed on Wednesday that David Moyes would not return to his role as manager following the expiration of his six-month deal.
The announcement arrived barely 12 hours after club co-owner David Gold said he hoped 55-year-old former Manchester United and Everton boss, Moyes, would remain in charge.
However, it seems former Manchester City boss Pellegrini is firmly on West Ham’s radar despite the salary demands.
The 64-year-old is currently managing Chinese side Hebei China Fortune.
The Chilean spent three years in England as Man City manager, winning the Premier League and two League Cups.
He has previously spent time in charge of Villarreal, Real Madrid and Malaga.
Sky Sports News understands Newcastle boss Rafa Benitez and Shakhtar Donetsk manager Paulo Fonseca are also on West Ham’s shortlist.