"He believes Augusta should admit women," Carney said. "Kind of long past the time when women should be excluded from anything."
Carney said Obama thinks it's "up to the club to decide," but that Obama told him he personally thinks women should be welcome.
Augusta's exclusion of women routinely has surfaced as a controversial issue, as the club is the longtime home of the prestigious Masters tournament. The issue has attracted particular attention as one of the club's sponsors, IBM, has a new female CEO, Virginia Rometty.
The last four CEOs at IBM, all male, have been invited to be members.
Mitt Romney, the Republican presidential front-runner, also said Thursday that he thinks women should be admitted at Augusta.
The chairman of Augusta National this week said the club will decide for itself whom to allow in its ranks.
"As has been the case whenever that question is asked, all issues of membership have been and are subject to private deliberations of the members," Billy Payne said when the inevitable question was asked Wednesday. "That statement remains accurate and that remains my statement."
The Associated Press contributed to this report.