The Chilean, who guided Manchester City to the Premier League title in 2013-14, is close to agreeing a three-year contract with the Hammers.
The former Villarreal manager will hold talks with David Sullivan, the West Ham joint chairman, on Sunday to finalise the deal.
West Ham were also in the hunt for Newcastle United boss Rafael Benitez, but it seems like the Spaniard will continue with the Tyneside club beyond the summer.
The report claims that Pellegrini earns around £10 million, and his contract includes a £5.1 million exit clause, which will expire at the end of the season.
It remains to be seen how much West Ham are willing to pay his compensation, but it is most likely that Pellegrini will command a salary that will make him the highest-paid West Ham manager.
He is scheduled to travel to London and will hold talks with the Hammers hierarchy to finalise the deal. Pellegrini is a vastly experienced manager, and he would be a fantastic appointment for the club.