Toure, 35, has been linked with a host of clubs since the expiry of his contract with the Citizens.
And the Hammers were mooted as a possible destination due to the presence of Pellegrini, with whom the Ivorian thrived under during their time at the Etihad.
However, Toure's agent recently claimed his client completed a medical in London, but ruled out West Ham, with a slight dig due to their current position in the Premier League table.
It's not West Ham, 100%.— Dimitry Seluk (@dmitriseluk) August 28, 2018
Yaya is a champion. The last place is not for him ???? https://t.co/eDGeI0EvFf
However, Pellegrini has since confirmed the club received the offer to sign the three-time Premier League winner.
"Unfortunately, they were the words of Yaya's agent," the West Ham boss said, when asked about Seluk's tweet. "I spoke to Yaya, I know him and appreciate him as a person.
"He is a very good player but in the moment, when we were doing our squad list, that position was covered for other players.
"We needed money to bring in players in other positions so we explained to Yaya clearly why he cannot come here.
"I hope he will find a good club, a big club because he is a very good player."