Bush is the former Florida governor, brother to President George W Bush and son of President George H W Bush. If he decides to run, a possible showdown looms with another familiar name Hillary Rodham Clinton, the former first lady and secretary of state and now a favourite hopeful of Democrats.
Various potential Republican candidates are still jockeying for position with a long two years remaining before 2016, and Boehner cautioned that the talk was a bit premature, but didn't shy from praising Bush.
Republican Sens. Marco Rubio of Florida, Rand Paul of Kentucky and Ted Cruz of Texas as well as Republican Paul Ryan, the party's 2012 vice presidential candidate, have been mentioned as possible presidential candidates along with a number of Republican governors.
New Jersey Governor Chris Christie, an early favourite, faces multiple investigations in a political retribution probe.
More From This Section
Bush, who speaks Spanish and is married to a Mexican-born wife, has prompted questions about his viability as a potential presidential contender by speaking with compassion for immigrants in the US illegally.
Hispanics have become a crucial voting bloc from Florida to Colorado to Nevada and other battleground states that decide the state-by-state race for the White House.
Bush enjoys the support of some of the Republican Party's most powerful insiders and financiers, who are hoping the party can woo Hispanic voters and rebound from candidate Mitt Romney's damaging rhetoric in 2012, when he spoke of "self-deportation" as a solution to America's immigration issue.