The first games to be played will be Aston Villa v Sheffield United and Manchester City v Arsenal.
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A full fixture set of fixtures will then be played on the weekend of June 19-21, with the games taking place behind closed doors.
Clubs are reportedly still discussing the idea at a meeting on Thursday, but it is understood all have agreed in principle at this stage.
On Wednesday, clubs unanimously voted to resume contact training, having started non-contact training last week.
Premier League players and staff will continue to be tested twice a week. Any players or staff to test positive must self-isolate for a period of seven days.
Liverpool currently sit 25 points clear at the top of the Premier League table while Bournemouth, Aston Villa and Norwich City are in the relegation places.
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