City skipper Yaya Toure was the target of monkey chants from a section of CSKA fans in the Champions League match in Moscow on Tuesday.
City, who won the match 2-1, will make an official complaint to UEFA about the chanting, and the governing body have confirmed they will investigate if the match officials confirm the incident.
UEFA told Sky Sports News: "We are awaiting the reports from the match which should land at some point today or tomorrow.
"Once received, the contents will determine whether a disciplinary case be opened. Should this be the case, we will communicate accordingly."
Toure spoke to the referee and City officials spoke to UEFA's match delegate after the match at the Arena Khimki and the club will make a written complaint on their return to Manchester.
Toure told Sky Sports: "I told the ref. I think it was unbelievable and very sad. We want to stop that.
"I think UEFA have to do a lot to try to stop it. Maybe close the stadium for a couple of games. As an African player, it is always sad when you hear something like that.
"For me, as captain, I was wearing an armband which said 'no to racism' and I was totally disappointed.
"It's stupid these people. I don't know, it just happens in football. It's unbelievable. They're stupid, they're just stupid. UEFA has to take action to right it otherwise I think they will just continue."
City manager Manuel Pellegrini added: "It's a pity and I hope we have the right measures."
FIFA vice-president Jim Boyce called on the Russian authorities to clamp down on racism.
"The Russian federation have got to assure - along with the Russian government - that these incidents are put to bed because it's happening too often. Too much abuse has been happening in many, many parts of eastern Europe," he said.
"Eastern Europe have problems, but we have problems in other parts of the world as well. It's got to be eradicated and the only way is to take serious action against the people who do it - don't allow them to watch football matches.
"I am absolutely appalled by events of this evening. I've always been outspoken against any form of racialism or sectarianism in sport."
The incidents in Moscow comes 18 months after Porto were fined £16,700 for their fans' racial abuse of Mario Balotelli during a Europa League game against City.
Piara Powar, executive director of the FARE Network (Football Against Racism in Europe), believes UEFA has been moving in the right direction on such matters.
He said: "UEFA have changed their rules and already this season sanctions are harder than ever before.
"For a first offence you face a partial stadium closure; for a second offence your stadium will be closed for a match.
"It's taken a long time to get here, but I think we are seeing some movement on the sanction side.
"In terms of education, I don't know how long that's going to take, to educate fans like we've seen at CSKA."