The Premier League season is set to restart on 17 June with Aston Villa v Sheffield United and Manchester City v Arsenal, the BBC reports.
A full round of fixtures would then be played on the weekend of 19-21 June.
There are 92 matches still to play, and the first to take place will be those the four teams involved have in hand.
Clubs are still discussing the idea at a meeting which will conclude later on Thursday but it is understood all have agreed in principle at this stage.
The Premier League was suspended on 13 March because of the pandemic and it will be 100 days after Leicester City’s 4-0 win over Aston Villa on 9 March that competition will resume, with games now behind closed doors.