Several Premier League club doctors have raised a number of concerns with league officials about plans to resume the season, BBC Sport learns.
An issue on which senior doctors sought assurance includes their own liability and insurance coverage if players contract the virus.
The Premier League has also been asked to provide some clarity about medical protocols, testing and player welfare.
The Premier League is hopeful of a possible resumption on June 8.
The club's 20 doctors have their own discussions about Project Restart – the label given to plans to resume action – with the aim of feeding their thoughts with the Premier League leadership.
A Premier League source told the BBC that he considered moving doctors a natural part of the process with clubs and a means of reaching "the best possible set of protocols".
They also confirmed that the league was talking to insurance companies about the liability of clubs and doctors, and that this would be discussed with government officials this week.
The Premier League is represented in a cross-sport working group of specialist doctors and public health officials who will meet for the second time in a week on Wednesday.
The panel is planning the health and hygiene measures that players, managers and club staff must agree to before training is complete, and then competition can resume, but only if the government considers it safe to do so.
The government is due to review its blocking measures later this week, with the Premier League meeting to vote on the plans next Monday. Several players and sports doctors have already expressed concerns about whether it is safe to return to action.
Eamonn Salmon, chief executive of the Football Medicine and Performance Association (FMPA), told BBC Sport that the opinion of doctors and physiotherapists at English football clubs about the recovery plans was mixed.
Speaking last week, he said: "I think our members' opinions will really be a kind of snapshot of society.
"There are those who think it can be done, there are those who doubt it and there are those who probably suggest that it is an impossible task.
"We have to wait, this is a waiting game all the time, it is such a changeable and fluctuating scenario in everyday life.
"This is just the beginning in some aspects, whatever the proposals presented, it is open to debate and for comments and opinions to contribute to it".
If training is resumed before the social distance rules are relaxed, BBC Sport understands that players will be tested for coronavirus twice a week and will be screened for symptoms every day.
All tests would be performed by health professionals in an NHS test unit that each club would have access to. The training camps will be optimized for social distance and high levels of hygiene.
- Players must arrive at kit training locations and wear masks at all times.
- They should not bathe or eat on the spot. If clubs want to provide food to players, they must be delivered to take to the players' cars.
- Only essential medical treatment would be allowed, with the entire medical team in full PPE.
- All meetings and reviews must take place virtually and off-site.
In Germany, where the Bundesliga is expected to become Europe's first major football league to return to competition, 10 positive results were returned from 1,724 coronavirus tests from clubs in the two main divisions.
Puppies are training in groups and testing is being done before a planned return to training as a team.
Measures including "isolation of the affected person" have been taken, DFL said.
The Cologne front-line team had no more Covid-19 infections after three people tested positive last week.
Bundesliga officials suggested a resumption on May 9, but the government postponed the decision and a restart may now be on May 16 or 23.