"I mean if that is what he decides to do, of course we would be very proud of him and excited for that," she told CNBC Meets' Tania Bryer.
Over the weekend, the former Florida governor also said he would release 250,000 emails early next year from his two terms in office and write an eBook outlining his governing policy on Sunday, sparking speculation that he is closer to confirming his decision to run.
Read MoreJeb Bush to 'actively explore' run for president
Bush Lauren, who is founder and chief executive of social business FEED, also said she was happy to stay out of political the arena rather than follow in the footsteps of grandfather President George H. W. Bush and uncle President George W. Bush.
"I feel like what we are doing here at FEED is public service, so I love that I have been able to carve out my way of doing public service whilst staying out of the political arena," she said.
FEED sells bags, accessories and apparel with measurable donations attached to each product and works in conjunction with partners Feeding America and the World Food Programme (WFP).
Bush Lauren, who married David Lauren, son of fashion designer Ralph Lauren in 2011, also set up the FEED Foundation, a non-profit arm of FEED Projects.
Read MoreAll signs point to Jeb Bush prepping for 2016 presidential run
Growing up in Texas, as part of one of America's most famous political families, Bush Lauren admitted that her upbringing was "privileged" but also "pretty normal".
"I think at the time I didn't realise how lucky I was. I always had a great education, a roof over my head, food, clothes but truly I had a pretty normal upbringing also. I grew up on the suburbs of Houston, I got a used car when I turned 16 which I was so lucky to get and grateful to get," she said.
CNBC Meets: Lauren Bush Lauren will air on 17 December at 23:00 CET