The Premier League is set for a decisive few days in establishing whether it is possible to resume and complete the current season.
Club officials will meet on Monday to continue talks on "Project Restart".
Prime Minister Boris Johnson did not mention professional sport in unveiling plans to reopen society on Sunday.
The government is expected to announce on Monday that some elite athletes can start an initial phase of restricted group training later this week.
That will depend on medical protocols being finalised and accepted.
Footballers have so far been limited to individual training.
On Monday, Alison McGovern, the shadow sports minister, wrote to Sports Minister Nigel Huddleston asking 20 questions about "Project Restart".
They request transparency around plans and medical protocols, health risk assessments, numbers of people allowed at games, measures if there are positive tests, personal protective equipment for medical staff, non-playing staff, referees and the media, and ticket refunds for fans.
"The government's recent media announcements have placed great emphasis on the morale impact of the return of the Premier League," McGovern writes.
"Leaving aside the focus on elite sport rather than grassroots participation, this strategy raises many questions. The public will rightly wish the government to be open about its plans."
A vote on whether to use neutral venues is not planned during Monday's Premier League meeting - a sign that an estimated six or seven clubs remain opposed to the idea.
But the talks represent a major step towards establishing whether there is an appetite for playing out the season.
League bosses do not believe there is wide support for scrapping relegation, and are confident there is a consensus for returning to training, regardless of when the permission to play again is given.
The league has been suspended since 13 March because of the coronavirus pandemic but is aiming to resume in June, with most clubs having nine games to play.
Culture Secretary Oliver Dowden is due to meet football authorities on Thursday.
Later this week, the Premier League will also hold talks with the Professional Footballers' Association and the League Managers Association after they have digested the medical protocols needed for a return to firstly phased training and then full competition, and have received feedback from their members.
On Sunday, the PM said people in England will be able to "play sports but only with members of your own household".
Dowden posted on social media that the government will "imminently allow" some sports like golf, basketball, tennis and fishing to resume "in the least risky outdoor environments", and only for those taking part alone or in their own households.
The Premier League still faces several challenges around "Project Restart".
A third, unnamed Brighton player tested positive for coronavirus on Sunday, after two others tested positive earlier in the pandemic.
Privately conducted coronavirus tests are reckoned to cost between £150 and £180 and it is understood the protocols being worked on in football insist on twice-weekly tests.
For the Premier League to complete the remaining 92 matches, that could be about 40,000 tests at a cost of about £30,000 a week.
Crystal Palace chairman Steve Parish, who is backing "Project Restart", told BBC One's Andrew Marr Show that initial plans to stage league matches again from June may prove unfeasible.
A vote on neutral venues is likely to be held later in May and 14 of the 20 clubs must vote in favour for it to be adopted.
Before voting, league bosses are also awaiting government guidance on the criteria for bio-security at events and ground-safety licensing, which is expected later this week.
Monday's Premier League meeting will feature a vote on whether player contracts are to be extended until the end of the rescheduled season.
European leagues have until 25 May to tell governing body Uefa whether they want to complete or cancel their seasons.
Premier League chief executive Richard Masters has previously predicted a loss of "at least £1bn" if the Premier League fails to complete the 2019-20 campaign.