The World Cup qualifying meeting between the sides was twice cancelled due to snowy weather this week and the 43-year-old is keen to avoid playing the fixture over the summer
The match had originally been set for Friday March 22 but was twice cancelled with the snowy conditions in the UK making the Windsor Park pitch unplayable.
And, with Fifa set to decide on a new date for the fixture, O'Neill has dismissed the idea of playing during the summer break.
He told reporters: "When we [Northern Ireland] come to talk about the new date, I will have to take into account that a game in June is well after the players' club season is over.
"If we play on one of the international dates in June that could be four to six weeks since the players were in regular football - well into their summer break. That would not be ideal.
"August is also an option but it would mean Russia cancelling their planned friendly with Argentina and I am not sure they would be willing to do that.
"If possible, I am going for a date in May as close to the end of the season as possible."