Football League chief calls for 'cool heads' over virus chaos
The second-tier Championship, League One and League Two last week suspended play until April 3 at the earliest in response to the pandemic.
Clubs are awaiting guidance on how to proceed, with concerns spiralling over the potential financial damage to smaller teams if the season is not able to finish.
There is also the issue of promotion and relegation to resolve if games cannot be completed.
A potential cancellation of Euro 2020 would open a window in the summer to wrap up the domestic season.
If that is not possible, there have been reports the current top two in the Championship -- Leeds and West Bromwich Albion -- would be promoted to the Premier League.
That could trigger bitter legal action if clubs are unhappy they did not get the chance to complete potential promotion-winning campaigns themselves.
All the speculation has led to an alarmist atmosphere around the English game but, with the EFL board set to meet for a further update on Wednesday, former Liverpool chief executive Parry urged teams to stay calm.
"These are indeed challenging times for the league, its clubs and the game as a whole," Parry said.
"However, now is the time for cool heads and calm reflection rather than speculation as we look to steer our competitions and clubs through this period of uncertainty."