The Premier League has contacted clubs to get their views on allowing up to 500 away fans at matches in the final two rounds of the season, the PA news agency understands.
Under the current Government plans, which are scheduled for a final review on May 10, up to 10,000 supporters could be permitted into football grounds from May 17.
The Carabao Cup final on April 25 welcomed the largest gathering of spectators since the coronavirus pandemic hit last year, as 8,000 fans descended on Wembley to watch Manchester City take on Tottenham.
However no supporters have been able to attend any Premier League matches since the country went into its second lockdown in December, and away fans have not been in attendance all season.
Richard Masters, the Premier League's chief executive, has written to clubs for their opinions on the possibility of including up to 500 away fans within the permitted 10,000.
In a letter to the clubs, reported in The Times, Masters said: "(The) Government has informed us that, as Covid-19 indicators continue to improve, it is planning to relax the 'no away fans' stipulation from the stage five guidance, governing the playing of our final match rounds in season 2020-21.
"The return of fans and ultimately full stadiums remains our primary goal; therefore our view is that we must accept the opportunity to host as wide a range of supporters as possible.
"That being the case, the executive proposes an away-ticket allocation of five per cent of available capacity (a maximum of 500 away fans) at round 37 and 38 matches, respecting the £30 away-ticket price cap."
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