The vote comes after calls to shift the tournament from the private club in Saitama province because of the rule, which allows women to play Monday through Saturday but bars them from becoming full members and from playing on Sundays.
The Tokyo Olympic organising committee sent a letter to the club on Thursday appealing for it to reconsider the policy.
The missive was sent on behalf of organisers, the Japanese Olympic Committee, the International Golf Federation and the Japan Golf Association.
"I think it's very important that the Kasumigaseki Country Club reach a conclusion as soon as possible," Olympic Minister Tamayo Marukawa told reporters on Friday.
"I certainly hope that they consider giving female members the same treatment as men," she said.
The 15-member club board will meet next Tuesday with a unanimous vote required to change the relevant bylaws, the Kyodo News agency reported.
Hiroshi Imaizumi, Kasumigaseki's general manager, told Reuters that the club would hold a board meeting next week but that the date and agenda had yet to be decided.
Both men's and women's tournaments will be held at the club in 2020, following the return of the sport to the Summer Games at last year's Rio Olympics.
Two of the most famous golf clubs in the world have changed their policies to allow female members in recent years.
In 2014, the Royal and Ancient Golf Club of St Andrews decided to allow women to join after 260 years of exclusion, and Augusta National, home of the U.S. Masters, ended its men-only membership in 2012.
(Reporting by Nick Mulvenney in Sydney and Chris Gallagher in Tokyo; Editing by Peter Rutherford)
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