Pellegrini, who is currently in charge of Chinese Super League club Hebei China Fortune, has recently been linked with a move to West Ham. While the Hammers are currently managed by David Moyes, the Scot's contract is due to expire at the end of the season and he is yet to be offered a new deal.
Earlier in the week, Moyes seemed to distance himself from becoming West Ham's permanent boss, saying, as quoted by Sky Sports: " "We'll have a chat next week and we'll see [whether I stay].
"It's been a tough job but a really good job, I've really enjoyed it and the players have worked hard when we came in, we had to get them in order a little bit and get them playing a bit better, and I think we've done that."
According to Marca, West Ham have held discussions with the Chilean and an agreement could be in place between the two parties for him to take over in 2018/19.
However, the report also claims that Pellegrini would be willing to cancel the agreement, if he's offered the opportunity to manage La Liga outfit Sevilla.
The Andalusians are looking to appoint a new sports director and Antonio Cordon, the current favourite for the job, knows and favours Pellegrini from his time at Villarreal.