The Premier League is set for a few decisive days to determine whether it is possible to resume and complete the current season.
Club officers will meet on Monday to continue negotiations on restarting the project.
Prime Minister Boris Johnson did not mention professional sport in presenting plans to reopen society on Sunday.
The government is expected to announce on Monday that some elite athletes may begin an initial phase of training in a restricted group later this week.
This will depend on the completion and acceptance of medical protocols.
So far, football players have limited themselves to individual training.
A vote on the use of neutral venues is not expected during the Premier League meeting on Monday – a sign that six or seven clubs are estimated to remain against the idea.
But the talks represent a big step towards establishing whether there is an appetite for playing the season.
League bosses do not believe that there is broad support for abandoning abandonment and are confident that there is a consensus to return to training, regardless of when permission to play again is granted.
The league has been suspended since March 13 because of the coronavirus pandemic, but plans to resume in June, with most clubs facing nine games.
Culture Secretary Oliver Dowden is due to meet football officials on Thursday.
Later this week, the Premier League will also hold talks with the Professional Football Players Association and the League Managers Association, after digesting the medical protocols necessary for returning to phased training and then the full competition, and will receive comments from its members.
On Sunday, the prime minister said people in England could "play sports, but only with members of their own home".
Dowden tweeted that the government "will imminently allow" some sports such as golf, basketball, tennis and fishing to be resumed "in less risky outdoor environments" and only for those who participate alone or in their own homes.
The Premier League still faces several challenges around Project Restart.
An unidentified third Brighton player tested positive for coronavirus on Sunday, after two others tested positive early in the pandemic.
Coronavirus tests carried out at private companies cost between 150 and 180 pounds and it is understood that the protocols being worked on in football insist on testing twice a week.
For the Premier League to complete the remaining 92 games, there may be around 40,000 tests at a cost of around £ 30,000 per week
Crystal Palace president Steve Parish, who supports Project Restart, told BBC One's Andrew Marr Show that initial plans to play league matches again in June it may not be viable.
A vote in neutral locations is likely to be held in late May and 14 of the 20 clubs are expected to vote in favor of their adoption.
Before the vote, league leaders also await government guidance on biosafety criteria at events and ground safety licensing, which is expected later this week.
Monday's Premier League meeting will include a vote on whether players' contracts should be extended until the end of the rescheduled season.
European leagues have until May 25 to tell UEFA whether they want to complete or cancel their seasons.
Premier League executive director Richard Masters previously predicted a loss of "at least £ 1 billion" if the Premier League fails to complete the 2019-20 campaign.