UEFA president Aleksander Ceferin could push for the delayed Euro 2020 finals to be staged in just one country, according to Karl-Heinz Rummenigge.
Any such move would cause a drastic redrawing of plans for the tournament just months out from its start, with 12 cities across Europe preparing to stage games.
The logistical implications would be enormous, with the need to find suitable team bases a major issue, while finding agreement on which country might serve as sole host may not be straightforward.
UEFA took similar steps last season to ensure the Champions League and Europa League campaigns could finish without further delay, but a month-long European Championship is on a different scale to those club competitions.
Yet the COVID-19 crisis could mean there are obstacles to staging the event as originally planned, and that could trigger contingency measures.
Quoted by German publication TZ, Bayern Munich chief executive Rummenigge said: "You shouldn't forget that the idea of this special hosting of the tournament came about when corona did not yet exist.
"At the time, it was an initiative of the EU Commission that wanted to have football shown all over Europe. But I know that the UEFA president Aleksander Ceferin – who is incredibly careful with corona – is thinking about whether it wouldn't make more sense in times of corona to play the tournament in just one country."
UEFA's expansion of the tournament to a 24-team event, starting from Euro 2016, means it is now close in scale to a World Cup, and the opening match is due to take place on June 11, with Italy and Turkey set to play in Rome.
Shifting the quarter-final stages of last season's club competitions to Lisbon and Germany meant they were able to be completed, with barely two months between decisions being taken and the games going ahead.
This is due to be the first time UEFA has held a European Championship in such a spread of venues. Ceferin referred to the Euros in December as "a tournament bridging the entire continent".
UEFA also said in November it intended to proceed with the tournament in its original format, albeit accepting that could change depending on circumstances.
It has since said decisions on how many supporters, if any, will be able to attend games, are set to be taken in March.
The semi-finals and final are scheduled to be held at Wembley Stadium in London, with other games in Baku, Amsterdam, Rome, Bilbao, Bucharest, Budapest, Copenhagen, Dublin, Glasgow, Munich and Saint Petersburg.