Everton and Liverpool are expected to vote on the dates of this summer's transfer window during a conference call this week.
Before the coronavirus pandemic struck, the transfer window in England was originally scheduled to open on June 8.
Premier League chief executive Richard Masters recently moved to confirm that the transfer window will not open until the season ends on July 26.
However, it is now understood that sides in the top-flight will discuss whether to open the window before the end of this season, at their latest Premier League shareholders meeting on Thursday.
It is also expected that clubs will discuss the option of extending the deadline in October, to allow more business to be conducted.
UEFA last month recommended that its member associations agree to close their summer transfer windows in unison on October 5.
The new guidelines issued by the governing body claimed they were hoping for a 'harmonised' end to the transfer window across Europe.
"The deadline for player registration for the group stage of the 2020/21 UEFA club competitions has been set to 6 October 2020,” a statement from UEFA read.
"As a result, the UEFA Executive Committee called on all member associations to adopt a harmonised end date to the upcoming summer transfer window, with this date set as 5 October 2020."
Associations around Europe may have up to 16 weeks a season for two registration windows under FIFA regulations.
The first registration period, traditionally the summer window, must not exceed 12 weeks, while the second, usually the January transfer window, is expected to last around 4 weeks.
For clubs wanting to utilise the full time available, they may agree to open the window before the season ends on July 26, but sides also have the option to close the window past the October 5 recommendation from UEFA.
