Premier League clubs will next discuss the future in an April 3 call, according to Sky Sports.
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There are nine full matchdays left to play this season, with Manchester City, Arsenal, Aston Villa, and Sheffield United having 10 to play.
The clubs are hoping to have more guidance from the government and other experts before the April call, and will not make any decisions until they know how they will affect the country.
Sky Sports News has been told a return date of June 1 is one of several dates put forward for consideration, but clubs did not discuss fixture modelling in detail during an emergency call on March 19.
The Premier League was initially suspended until April 3 before the clubs extending the suspension to April 30 on Thursday.
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