Kallen admitted that UEFA had drawn up a contingency plan and worked it through with French authorities.
"We [may] postpone the match till the next day or the day after that. Ideally, it will take place three hours before the scheduled game. The question is: with or without spectators," he said in an interview due to be published Wednesday.
Kallen said that if UEFA makes changes on very short notice, football fans will not be able to rebook hotels and get to the venue on time.
Security concerns over mass gathering in France were raised after a series of terrorist attacks, including outside the Stade de France stadium in Paris last November. Stade de France is one of the ten stadiums where Euro 2016 games are set to be held between June 10 and July 10.