The 31-year-old Ivory Coast international was reportedly subjected to a string of abusive and racist messages hours afters reactivating his Twitter account on Monday.
A Greater Manchester Police spokesman said: “GMP can confirm we have received a number of complaints regarding racist tweets directed at Manchester City Football Club player Yaya Toure on Monday, November 3 2014.”
Anti-racism charity Kick it Out was one of the complainants, tweeting on Monday: “We are informing the police of racist tweets directed @yayatoure earlier this evening and offer him our full support.”
Toure closed down his Twitter account five months ago in order to concentrate on the Ivory Coast’s campaign at the World Cup in Brazil.
Announcing his return to the social networking website following City’s 1-0 win over Manchester United on Sunday, he tweeted: “Great to be back on twitter after a good win yesterday. Now my focus is on the next game… Happy Monday everyone!!”
He received several abusive messages from other Twitter users in reply.
City manager Manuel Pellegrini said on Tuesday that he did not think the matter would affect Toure’s focus.
“I think Yaya is an experienced player. He is always trying to fight against those things, but I don’t think he will have any problem about that, to play in the way he knows to do it,” Pellegrini told a press conference.
“I read the news about what happened, but I think the people in charge will do the right things.”
Toure was subjected to racist abuse by fans of CSKA Moscow during a Champions League match last season and City have a home fixture against the same club at the Etihad Stadium on Wednesday.
Following similar incidents, CSKA were punished by European governing body UEFA, who ordered them to play three matches — subsequently reduced to two on appeal — behind closed doors.
Under the terms of the punishment, the Russian champions will have no supporters present at Wednesday’s match.