Premier League clubs will vote on proposals for a return to contact training at their next shareholders' meeting on Wednesday.
It is understood that consultation with players and managers is taking place between now and then.
The UK government's guidelines for contact training have been published, and it is anticipated that clubs will gradually build up the level of contact, from 'clusters' of two to three players initially, through larger groups before a return to full team training.
Testing will continue on a twice-weekly basis. The latest round of Covid-19 testing is taking place on Monday and Tuesday, with results expected on Wednesday.
Crystal Palace winger Andros Townsend says players are "desperate" to return to contact training and that he is encouraged by the results of the Premier League's testing regime for the new coronavirus.
The second round of testing returned two positives - with Bournemouth saying one of their players was now self-isolating - as the government issued guidance on the next step for athletes to resume close-contact training.
"We're desperate to get back to normality and contact training," Townsend told Sky Sports
"At the start of the week you're worried about being near other players, but as the days go on you get more and more comfortable with each positive test.
"If it was two people from the same club (who had tested positive) you'd start to ask questions about how it had spread around the training ground.
"But the fact it's at two different clubs and they've kept it from spreading shows that we're in the safest workplace in the country and it gives us confidence to move on to the next phase of testing."
Premier League players have returned to non-contact training in small groups with their clubs and stage two of the government's guidance will allow close quarters coaching and tackling in team sports.
"We're training in groups of eight, so there's 16 players from the squad I just haven't seen," Townsend added.
"Hopefully, with each successful round of testing, we can get a few more players back into training and some time next week we can move on to phase two."