The president of the Italian FA wants the competition to resume on 17th May, but he has not rejected alternatives. He himself admitted in an interview with 'Domenica Sportiva' that he would not be against playing in September or October if necessary.
"Ending the season in September or October? It's an option. Right now, a possible date to restart the league is 17th May, but I must say it is only a possiblity. The best thing would be to not only not affect the 2019-20 campaign, but also to prevent affecting the 2020-21 one," he assured.
Be clear, therefore, that there are two options. The first is that all leagues manage to finish and the start of next season is unaffected. The second is that weeks or even months of next season will have to be used up to complete this season's games. Gravina is open to both possibilities.
His flexibility will go down very well at UEFA. The European organisation's priority is for all leagues to be completed. They do not want seasons being ended prematurely without all the fixtures being played.