Government officials will hold a meeting with the Premier League next week and are "hopeful" a plan can be agreed to see games resume.
Everton, Liverpool and the other 18 top flight clubs are due to hold a video conference on Monday to discuss in further detail the various proposals laid out under Project Restart, which aims to see matches return next month.
Oliver Dowden, secretary for digital, culture, media and sport, has this morning said the government want football to come back because it will be "good for the nation" but he stressed that public safety "must come first".
He will talk to the Premier League, the EFL and FA next week about progressing plans for games to resume behind closed doors.
The Premier League clubs will not vote on restart plans on Monday, as initially believed, but clubs may be asked to approve some elements of the proposals.
Uefa has asked for all domestic leagues to inform them of all plans by no later than May 25.
Players, including Seamus Coleman and Jordan Henderson, are scheduled to hold talks with the Premier League later next week but will not be involved in Monday's discussions, which will come after prime minister Boris Johnson addresses the nation to unveil his plans for how the country come come out of lockdown.
Dowden told BBC's Today programme on Radio 4: "It [Football] has not got the green light.
"I met with the Premier League a couple of weeks ago. We've had two sessions, the first of which I chaired with the deputy chief medical officer, looking at how we could do this in a safe way.
"But it's not just the Premier League, the rest of football and other sports that could, potentially, take place behind closed doors.
"Public health and safety will come first and if we can get a plan that works then I would like then I would like us to go ahead with it because, I think, it will be good for the nation and good for football as a whole.
"I will certainly be meeting, on Thursday, with the Premier League, the English Football League and the FA and I'm really hopeful we can get this up and running.
"But public safety must come first so it's only if we are confident of that, that will be able to proceed."
Yesterday, it was confirmed that Liverpool have re-opened Melwood for players to work on their fitness but under tight restrictions.
The Premier League, meanwhile, are not commenting on reports that they want a resolution over all players coming to the end of their contracts, by June 23.
Retained and released lists are usually submitted to the Premier League by the third week in May.
