The Ivorian has been strongly linked with a move to the Hammers during recent weeks.
Part of the reason for this was that Toure and Pellegrini had previously worked together when City went on to win the top-flight during the 2013-14 season.
While the Premier League clubs are no longer allowed to buy new players, following the August 9 deadline, Toure can still be signed by a Premier League club as he is a free-agent after having departed from Manchester City at the end of last season upon the expiration of his contract.
As one of the greatest Premier League players of the modern generation, it is very surprising that the 35-year-old has not been able to find a club as yet.
Despite being on the wrong side of 30, Toure is still hungry to play in a top League and his agent Dimitri Seluk even revealed that he would be willing to play for an ambitious club even if they offered him a salary of £1 as reported by Goal.
West Ham have abundant options in midfield this season with Robert Snodgrass, Felipe Anderson, Michail Antonio, Mark Noble, Pedro Obiang and Carlos Sanchez all available to Pellegrini.
When responding to rumours linking Toure with a move to the London Stadium, Pellegrini said as reported by Goal: “Yaya Toure is a good player, but in this position, we have our players.
“He will always be a good player, but for the moment he is not for West Ham. For the moment, the squad is complete.”