The 64-year-old former Manchester City boss is the frontrunner to succeed David Moyes at the London Stadium.
West Ham joint-chairman David Sullivan said the club needed to move in a "different direction" with a "high-calibre figure". There has already been contact between the parties and Pellegrini is expected to have a face-to-face interview with West Ham co-owner David Sullivan in the coming days.
Despite being under contract at Hebei through to the end of 2018 and with a reported £5.3m release clause, the CSL club confirmed on Saturday Pellegrini was no longer in his role.
And, in a statement on their Weibo account on Saturday, Hebei China Fortune said: "We have reached an agreement with Manuel Pellegrini that he will no longer serve as team manager.
"Here, the club would like to express its sincere gratitude to Mr Pellegrini for his contributions and we wish him well in his future work life.
Pellegrini coached at Villarreal, Real Madrid and Malaga in Spain before taking charge of Manchester City in 2013, going on to win the 2013/14 Premier League title as well as the League Cup twice before his departure.
The 64-year-old Chilean left the Ethiad Stadium in June 2016, where he was succeeded by Pep Guardiola, but was soon back in work at Hebei.