Montagliani, who is also one of FIFA’s vice presidents, is part of a group set up by the world football governing body to deal with the repercussions of the virus on the football calendar.
Major international football tournaments including EURO 2020, Copa America and CONCACAF Nations League, originally set for this summer, have had to be postponed because of Covid-19, which has infected close to two million people globally and killed more than 123,000 people.
International games set for March and June have already been pushed back and now those set for September, October and November might have to be rescheduled as well in order for domestic football across the globe to be completed.
Asked by the Associated Press if he saw national teams playing in 2020, he said: "I personally think that might be a bit of a challenge, not so much because of just the health issues around the world and the various degrees of preparedness, but also committing to international travel as soon as we come back.
"I think that domestic football is a priority. September is still in the books, but I would garner to say that I'm not sure it's there on solid ground the way things are trending right now."