Premier League clubs hope to give their players the go-ahead to return to training in small groups this week.
But there is a growing feeling the intended 12 June date for matches to start again will need to be pushed back.
A vote is due to take place on training and medical protocols when the 20 top-flight clubs hold their next meeting on Monday.
If passed, players would be able to train in groups of five from Tuesday.
That would be on condition they observe social distancing rules and adhere to a series of strict criteria, which include getting changed at home and driving to training grounds on their own.
At least 14 of the 20 clubs must agree that safety protocols are sufficient for the plan to be approved.
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Last week, the government said it had "opened the door" for the return of elite sport, but several hurdles remain before the Premier League can resume behind closed doors.
Clubs have been carrying out coronavirus testing this weekend to ensure there is no further delay, but a number of players - including Newcastle United defender Danny Rose and Watford skipper Troy Deeney - have expressed concerns about returning.
Players have been asked to sign waivers and it is understood the Professional Footballers' Association has offered to get the agreements legally checked if anyone is uncertain.
Club officials have been holding high-level meetings because the legal liability for any player who became seriously ill would fall on them.
It is anticipated a three-step return to action will be implemented. It is hoped to move into the second phase at the beginning of June, which would involve training in larger groups, before a return to contact training.
At the meeting on Monday, clubs will also be updated on talks with police and safety committees over the request to play matches at their own stadiums rather than at neutral grounds, as initially proposed.
They will also receive a report on the return of Germany's Bundesliga and will have been heartened to learn there were no instances of fans turning up at stadiums in significant numbers.
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Manchester City forward Raheem Sterling said on Sunday that players would need a "full four to five weeks" of training before returning to competition.
Newcastle manager Steve Bruce had earlier told the Sunday Telegraph the timescale was "at least six weeks", adding: "I don't see how we can play games until the back end of June."
The Premier League is thought to be relaxed, viewing the restart as more important than the actual date.
It also knows that while Uefa hopes domestic leagues are completed by 31 July, there are spare days in August free from European competition to allow outstanding fixtures to be played.
What happens next?
- 18 May: Next Premier League meeting
- 19 May: Players may return to group training under socially distancing protocols
- 25 May: Uefa deadline for leagues to have finalised plan for restarting seasons
- 1 June: Government date for possible return of elite sport behind closed doors
- 12 June: Premier League aiming to return with first fixture
Further talks in the EFL
In addition to the Premier League meeting, League One clubs will hold further talks about how to proceed with their season after a meeting on Friday ended in deadlock.
Many clubs want the season to end now because of the costs involved but at least seven - including Peterborough, Sunderland, Ipswich and Portsmouth - want to continue.
They hope to have a plan to put before Wednesday's meeting of the EFL board, which will also have to assess League Two's proposals for terminating the season.
It is thought unlikely the request to not relegate anyone to the National League will be endorsed, with a number of Championship clubs making it clear they would not agree with any decision that undermines the concept of promotion to the Premier League.