In an interview with People magazine, the younger Bush said Clinton -- a former first lady and U.S. senator from New York -- is "unbelievably accomplished."
Barbara Bush, 31, said however, she would not guarantee she will vote for Clinton, who sought the Democratic presidential nomination in 2008.
"I don't know who she'd be running against," Bush said.
She said she is a supporter of same-sex marriage and is not affiliated with a political party, NBC News reported.
The interview -- which mainly focuses on her work as chief executive officer of Global Health Corps -- is scheduled to run in the Aug. 26 issue of People, where Barbara Bush's sister, Jenna, works as a correspondent.
Global Health Corps, a non-profit that operates in several countries in Africa, has collaborated with former President Bill Clinton's Health Access Initiative and first lady Michelle Obama's Let's Move fitness campaign, NBC said.
"We want results. We work with people doing great work," Bush said.
Benedict Cumberbatch's dramatic reading of R. Kelly lyrics is just what you need
Kate Middleton recycles dress at movie premiere