Bush, who had dismissed suggestions of a presidential run, spoke openly about in interviews and his longtime political adviser, Sally Bradshaw, said Tuesday in an interview with The Washington Post that Bush "will seriously think about it."
The 60-year-old son and brother of presidents George H.W. Bush and George W. Bush had dismissed his own presidential bid in two previous elections, but now says he's more open to the possibility.
"I'm not saying yes. I'm just not saying no," Bush said on MSNBC. "I've accomplished some things in my life that allow me now to, to have that kind of discretion, to be able to think about it."
Almost as soon as Bush began his promotional tour for his book, "Immigration Wars," Republicans questioned his motives and timing, the Post said. The book proposes giving legal status to illegal immigrants but requiring them to return to their home countries before pursuing citizenship, catching many Republicans by surprise.
Bush has long favored granting illegal immigrants a chance to gain citizenship and has expressed concern that Republicans favoring more restrictive approaches were alienating Hispanic voters.
"This proposal caught me off guard, and it undercuts what we're trying to do," said Sen. Lindsey Graham, R-S.C., a member of a bipartisan working group on immigration.
Bush and his aides said Tuesday he wrote the book last year after the fractured GOP presidential primary, in which eventual nominee Mitt Romney voiced support for "self-deportation," and Bush was looking for political middle ground.
"We wrote this book last year, not this year, and we proposed a path to legalization, so anybody that had come illegally would have immediately a path to legalization," Bush said on MSNBC "If you can craft that in law, where you can have a path to citizenship where there isn't an incentive for people to come illegally, I'm for it."
GOP strategist Ana Navarro told the Post Bush was victimized by bad timing.
"The partisan divide got a lot narrower, a lot faster, than Jeb anticipated," Navarro said.