Uefa has called an emergency meeting for Tuesday in which the possibility of postponing Euro 2020 by one year is an option being discussed.
European football's governing body will hold video conference meetings to discuss its response to the coronavirus outbreak.
Those discussions will cover all domestic and European competitions, including Euro 2020.
Euro 2020 is due to take place from 12 June-12 July at venues across Europe.
Uefa has invited representatives of its 55 member associations, plus the boards of the European Club Association, the European leagues and a representative of world players' union Fifpro.
The Women's Euros are due to take place in England from 11 July-1 August 2021.
Why is it up for discussion?
On Thursday, La Liga became the latest European league to be suspended because of the coronavirus outbreak.
The Spanish top-flight has been suspended for "at least the next two rounds of matches".
In addition, the Danish Football Association has cancelled all football activities in the country for two weeks while the Netherlands' Eredivisie has been suspended until 31 March.
In Italy, Serie A is suspended until 3 April, with the country in lockdown and two players - Juventus' Daniele Rugani and Sampdoria's Manolo Gabbiadini - having tested positive.
Matches in the top two leagues in France are being played behind closed doors while two Europa League last-16 first-leg fixtures scheduled for Thursday have been postponed and a number will be played behind closed doors, including Manchester United's trip to Austria to face LASK.
Manchester City's Champions League last-16 second leg fixture against Real Madrid, due to take place on Tuesday, has been postponed.
As it stands, the Premier League is to continue as usual despite three Leicester first-team players having self-isolated after showing symptoms.
In addition to moving the Euros, BBC Sport understands another option is playing the tournament but using the slots reserved for pre-tournament friendlies to decide the play-offs. Or it could go ahead without play-off teams as a 20-team tournament.
Four nations were due to qualify for the tournament from the play-offs in matches starting later this month. Both Northern Ireland and the Republic of Ireland are in the play-offs
It is understood the preference would be to complete the Champions League and Europa League.