Toure was subjected to racist taunts by CSKA supporters when the clubs met in the Champions League and they will face off in the same competition once again after being pitted together in Thursday's draw.
Toure was furious with the abuse and even suggested black players could boycott the 2018 World Cup in Russia if the country did not get to grips with the issue.
CSKA were punished with a partial stadium closure by European governing body UEFA and sanctions were increased to full closure after a further offence in another match.
That means CSKA will be playing behind closed doors at the Khimki Arena in their first home match of this year's competition.
That punishment will have been served by the time City visit on October 21, but Pellegrini expects Toure to be prepared to play.
"He does not have a problem to go to Moscow," Pellegrini said.
"At that moment he said what he thinks about it and every one of us supports him because I don't think those things can happen on a football pitch. This year Yaya doesn't have a problem."
Asked if he had spoken to Toure about the matter, Pellegrini said: "I don't think it's important to continue the same thing.
"That happened last year and UEFA has rules not to allow to those things so I don't think it's good to continue with that."