Football Association chief executive Mark Bullingham admits "things will get much more complicated" for the game's administrators if the current season is forced to go beyond June 30 because of the coronavirus pandemic.
The FA, Premier League and EFL are treating the completion of the English domestic season as a "priority".
However, the decision on Tuesday to push Euro 2020 back to the summer of 2021 has created extra space in the calendar to do so, with the Premier League and EFL having suspended competition until April 4 and 3 respectively.
The EFL board meets on Wednesday, with a Premier League meeting set to take place on Thursday to hold further talks on next steps.
Bullingham admits going beyond June 30 – the point at which player contracts expire and which marks the official end of one season and the start of another – could present problems, but says "nothing is off the table" in terms of a finish date.
"Clearly, things get much more complicated after June 30, but I would say nothing is off the table right now in the discussions being talked about both internationally and domestic level," he said.
"No one knows exactly what is going to happen and we have got many different scenarios which I won't go into in detail but clearly moving the tournament in the summer does potentially create more space for the domestic season to finish, which is everyone's priority."
It is understood dates of June 24 and June 27 were pencilled in, but not officially confirmed, for the Europa League and Champions League finals during the UEFA meeting on Tuesday.
Asked whether the FA Cup could be scrapped to help get the season completed, Bullingham said: "Within the context of that, clearly from our point of view, the FA Cup is incredibly important.
"We are talking the priority being that, whenever football can be played again, to complete the domestic season, we are talking about both the league and the FA Cup."
Scotland are due to face Israel in the play-offs, but Maxwell admitted it was "difficult to envisage a situation" where the games would be able to go ahead in June.
Northern Ireland take on Bosnia and Herzegovina in the play-offs.
Irish FA chief executive Patrick Nelson added: "At this point we can't be sure that we will be back playing football by then but that is the initial plan laid out by UEFA."
Gary Owens, interim chief executive at the Football Association of Ireland, said plans would immediately get under way regarding the four fixtures set to be hosted in Dublin during the Euros.
He said: "UEFA has made the right decision today in the interests of the health and well-being of football players, fans and staff alike.
"We support this decision and we look forward to working with all our stakeholders on reorganising UEFA Euro 2021 for Dublin next year.
"We would like to thank all our partners – the government, Dublin City Council, Aviva Stadium and all the agencies and partners who have worked really well with us on the UEFA Euro 2020 project for the last few years.
"We have agreed with these partners that we will now begin to plan together for the four UEFA Euro 2021 games here next year which will be the centenary year of the FAI."
The Football Association of Wales also backed UEFA's decision.
