Toure is available on a free transfer after leaving City at the end of the 2017-18 campaign, and it is understood that the experienced midfielder is keen to remain in the Premier League.
The 35-year-old is still believed to have a good relationship with Pellegrini following their time together at the Etihad Stadium, meanwhile, but the West Ham manager has revealed that he is not looking to sign the Ivorian.
"At the moment our squad is good," Pellegrini told reporters when questioned on Toure ahead of Saturday's Premier League clash with Bournemouth at the London Stadium.
"Yaya Toure is a good player, he will always be a good player, but for the moment he is not for West Ham."
Toure scored 79 times in 316 appearances for City during his time at the club, but failed to register in 17 appearances for the Citizens last term.