Pellegrini has left his role at CSL side Hebei China Fortune and is expected to sit down with West Ham co-owners David Sullivan and David Gold on Monday to hold further talks over taking over at the club.
The Chilean was one of the names on a four-man shortlist drawn up to find a replacement for Moyes and according to 'The Telegraph', the 64-year-old could attempt to use his good relationship with Toure to bring him with him to the club.
Toure is available on a free after ending his eigth-year spell at City and West Ham are known to be big fans of the Ivorian, having previously tried to sign him.
Pellegrini and Toure previously worked together at City and with the 35-year-old having reportedly turned down lucrative offers from the Middle East with the intention of staying in the Premier League, a move to West Ham would appear to tick a lot of boxes.