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."
Despite the obvious uncertainty and complications caused by the pandemic, Bullingham maintains everyone wants to see a proper conclusion to the 2019-20 campaign.
"We would all like, including all the international federations, the domestic season to be finished - that is one of the main reasons for delaying the Euros to allow, if the virus gets under control, a window to potentially finish the season," Bullingham told Sky Sports.
"At the moment we don't know what's going to happen. We are planning for every eventuality so we can react but the most important thing is people's health.
"Football is not our number one priority right now as a nation so clearly we have to work with everyone to make sure we bring this pandemic under control and then we work out how football can fit in as and when that is done.
"We are building up every scenario plan and every eventuality so when we get told football is safe, we will react accordingly."
Bullingham reiterated Wembley's desire to host seven matches at the tournament - including the semi-finals and final - and praised football for being "especially united".
FIFA president Gianni Infantino said the postponement of Euro 2020 until next year would be formally accepted on Wednesday.
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