Lillo, 54, left his post as coach of Qingdao Huanghai last week with the Chinese side claiming he was returning to Spain to look after his “seriously ill” mother.
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Manchester City did not replace Mikel Arteta when he left his role as Guardiola’s assistant to become Arsenal manager last December.
The Mirror claimed the pair had a difference of opinion on the direction of the midfielder’s career after Toure joined Chinese second division club Qingdao Huanghai in May.
The former Ivory Coast international, who has not played since December following a three-month stint with Olympiakos in Greece, is expected to make his debut on Saturday when Qingdao host Zhejiang Greentown.