Former US secretary of state Condoleezza Rice broke the Augusta glass ceiling in 2012 when she and financier Darla Moore became the first women members at the club, established in 1933, which hosts the 81st Masters tournament from today.
A third woman, IBM chief executive Virginia Rometty, joined the club in 2014, but when asked about the sparsity of female faces, Payne indicated that more women would be invited to join.
"Well, of course, we would not give you the profile of our incoming members before they know about it," he told a news conference yesterday.
Payne's predecessor as chairman, Hootie Johnson, resisted pressure to open the club to women, rejecting charges of sexism and saying a private members' club had the right to decide who can join it.
Augusta National has around 300 members on an invitation-only basis and no public list of names exists, although some of the world's richest and most influential people including Bill Gates are known to be among them.
The club is home to the Masters, the only major golf tournament played at the same venue every year.
However, Payne refused to be drawn into controversy over golf-loving current US President Donald Trump.
A favorite to win the Masters this week, Rory McIlroy, had to defend himself for playing a round of golf with Trump in February.
Trump's presidential campaign was nearly derailed last year by sexual harassment charges and his boasts about groping women.
In contrast, McIlroy has taken a pro-woman stand in the battle for golf club membership, notably at Muirfield in Scotland, where members voted 80% in favor of admitting women earlier this year.
"Several presidents, including one who was a member here, have been significant advocates and players of golf, and I think it's only natural that someone who loves the game would espouse and be proud of that association," Payne said.
"I'm not the one to judge, whatever, how his (Trump's) other remarks may have some influence on the game of golf, which is where my interest level resides exclusively.
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