ESPN reports that the original restart date of June 12 is, however, set to be scrapped, after clubs insisted on three weeks of full-contact training before playing.
Football has been on hold since the start of March due to the COVID-19 outbreak.
Clubs will have meetings this week to determine the restart date, which is likely to be a Friday night.
Premier League chiefs are now eyeing June 19 or June 29.
Players returned to training last week, but sessions are limited to small groups and low-contact drills.