The Sun says the Hammers have held talks with Toure but are reluctant to offer him a Premier League lifeline.
The Hammers were hoping to sign the City legend after his contract ran out this summer.
The 35-year-old has since launched an astonishing personal attack on City boss Pep Guardiola.
A Hammers source said: “Manuel Pellegrini might like him but Toure is perceived as by some others as having too much baggage.
“There are worries he might actually disrupt the dressing room and there is also little time for his agent.
“The comments about Guardiola have made them think twice, and they also wonder if he still has it in his legs.
“It would take a lot of convincing from the new manager, who is currently focused on a lot of other things."