The Premier League will hold an emergency meeting on Thursday to establish plans for the remainder of the season.
It is believed clubs will have more information by then after a UEFA European football stakeholders meeting on Tuesday.
As it stands, no Premier League fixtures will take place until April 4 at the earliest, with the Football League also suspending all games until April 3.
The measure to postpone Premier League football was agreed at an "emergency club meeting" on Friday and in light of Arsenal boss Mikel Arteta and Chelsea midfielder Callum Hodson-Odoiconfirming they had tested positive for the virus.
Some clubs believe the season can still be completed if games start again on April 4 but others think it is more realistic to start preparing for the possibility of there being no top-flight football until the start of next season in August.
One senior source at a Premier League club says he believes there is a "75 per cent chance this season will not be complete".