A final decision will be made on July 12 and, should the Government decide to press ahead with that plan, it will mean capacity crowds are allowed at sporting events once more from July 19.
Wimbledon's Centre and No1 Courts will be at maximum capacity from Tuesday this week, but a full football stadium has not been seen in the UK since before the pandemic began in March 2020.
The Government also announced that Covid passports would not be required by law to dictate entry to events, but that organisations could opt to use them. The Premier League have previously indicated that they would be open to doing so.
Regardless of the criteria, the Premier League have given the news a warm welcome.
In a statement reacting to the announcement from the Prime Minister, the Premier League said: "Fans have been hugely missed so we welcome today's announcement by the Government, and are looking forward to full stadiums in the 2021/22 season.
"As we move towards a Government decision on Step 4 of the roadmap and beyond, we will continue to work with football stakeholders and relevant public authorities to ensure that the return to full capacity is done in a way that keeps everyone safe."
The new Premier League season begins on Friday, August 13, with newly-promoted Brentford hosting Arsenal.
As well as the top-flight welcoming the decision, EFL chief executive Trevor Birch said: “The EFL welcomes today’s positive announcement by the prime minister that capacity restrictions are expected to be lifted later this month, which will allow us to finally press forward with our plans to see a full return of fans to EFL stadiums from the start of the new EFL season in just four weeks’ time.
“Football has been planning for this outcome since the outset of the pandemic and having been forced to endure empty stadiums since March 2020, the message from EFL Clubs is that we are ready to re-open and welcome fans back in numbers.
“From the EFL’s own participation in the Events Research Programme and our Club’s extensive experience built up over many years, we are confident that all our Clubs can successfully manage large scale events and we will continue to work with the Government on the guidance that will help support their matchday operations.
“Today’s developments, of course, have been made possible by the staff at the NHS and countless medical experts and scientists who have helped to develop and roll-out the vaccines. On behalf of the League and its membership, I would like to take this opportunity to thank you for playing such an important role in helping re-open our sport and wider society.”