Toure left Manchester City on a free transfer at the end of last season and had been linked with move to West Ham to play under his former manager Pellegrini.
The 35-year-old has since undergone a medical with his new club, although the midfielder's destination is still unclear.
Earlier this week, Toure's agent Dimitry Seluk said that his client would not be joining West Ham due to the fact that the midfielder "is a champion".
Pellegrini has dismissed Seluk's tweet though, and suggested that West Ham could have signed the Ivorian if they had wished.
"Unfortunately they were the words of Yaya's agent. 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," Pellegrini told reporters.
"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."