Toure, who is in the final six months of his contract at City, has returned to the starting line-up after initially being frozen out by manager Pep Guardiola following a row with his agent Dimitri Seluk.
Seluk mentioned Suning's offer before insisting the Ivorian midfielder is happy at the Etihad Stadium.
Seluk told Sky Sports: "Yaya wants to play at the highest level. He's happy at Manchester City. Yaya likes football more than money."
Clubs in China, boosted by huge transfer funds, have already made their mark in the window after signing three Chelsea players, Ramires, Oscar and John Obi Mikel.
The Chinese Football Association has now placed restrictions on the number of foreign players a team can field in a game.