Premier League clubs could vote to end the early closure of the summer transfer window at their next meeting on 12 September.
Two years ago, the top flight voted to close it before the start of its season to try to minimise squad disruption.
However, other European leagues did not follow suit and could still buy or loan players from Premier League sides.
They had until 2 September this year to conduct transfers, compared with 8 August for the Premier League.
As reported by The Times, the issue will be raised at the meeting of Premier League chairmen and chief executives next week.
A vote on again being aligned with the rest of Europe could take place at the meeting or may be delayed until the next time they get together in November.
The Premier League is believed to be neutral on the issue and is happy to facilitate any discussion or vote that the clubs may choose to have on it.
Last time around, 14 clubs were needed to be in favour of amending the transfer window whereas now a simple majority of 11 would be needed.
Of the clubs still in the top flight, Manchester United, Manchester City, Watford and Crystal Palace voted against an early closure in September 2017.
It is understood Liverpool now want a return to the old system, while Everton are believed to have sympathy with those clubs who want to align with the European deadline and would be prepared to hold talks on the issue.