The Premier League are keen for clubs to agree to stage two of Project Restart which would include full-contact training by the end of next week.
Clubs voted unanimously on Monday to resume to training in small groups this week.
However, since then, N’Golo Kante and Troy Deeney have both refused to return over health concerns.
The Times reports that the Premier League may struggle to convince players about the safety of full-contract training, with many still holding reservations.
For the Premier League to resume as it hopes to in mid-June, it needs clubs to move quickly into full-contact training in large groups so they can prepare for matches.
A return date of June 12 is still being targeted, although any further delays could see that date pushed back.
Coronavirus is having an impact across sport in Europe, with football league schedules suspended in several countries, including in England, Spain and Italy. But what happens next?
– The Premier League clubs are set for more talks with a key vote over the next steps regarding training.
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The Premier League are waiting for the government to issue guidelines on how elite sports can resume full-contact training in order to vote on stage two of Project Restart.
In a bid to offer assurances, there will then be a series of key presentations to players, managers and club officials but league officials are aware that sceptical players will need far greater reassurance before being prepared to agree to full-contact training than they were given during last week’s talks over the first return to training.
There is a particular concern among some players from BAME (Black, Asian and minority ethnic) backgrounds because coronavirus victims in the UK have been disproportionately from those backgrounds, which were cited by Deeney when explaining his decision to swerve training.