If it were up to former US president George W Bush, a third member of the Republican family dynasty – his younger brother Jeb – would run for the White House.

Jeb Bush, the former two-term governor of Florida, has acknowledged that he has not ruled out the idea of a 2016 presidential candidacy.

“I hope Jeb runs,” his older brother told CNN on Thursday. “I think he would be a great president.

“I have no clue what’s on his mind and we will talk when he’s ready. I noticed he’s moving around the country quite a bit.”

Indeed, 61-year-old Jeb Bush has rolled up to several political, educational and civic events across the nation in recent weeks, taking the pulse of various groups as he mulls his political future.

He sent a jolt through the Republican political establishment last month when, during a commemoration in Texas of his father George HW Bush’s presidency, he promised he will decide by year’s end whether he will seek the White House.

Most hopefuls are expected to file candidacy papers shortly after the congressional mid-term elections this November, and several polls show Jeb near the top of Republican prospective candidates.

According to an ABC News/Washington Post poll released on Wednesday, Bush is on par with Senator Rand Paul, followed closely by former candidate Mike Huckabee, congressman and 2012 vice-presidential candidate Paul Ryan, and New Jersey Governor Chris Christie.

Hillary Clinton, President Barack Obama’s first secretary of state, dominates the Democratic side, and the same poll showed her beating Bush 53% to 41% in a hypothetical match-up.

If they each won their party’s nomination, the 2016 election would feature the same two families as in 1992, when Bill Clinton ousted incumbent, the elder George Bush.

Dynasty fatigue may come in to play, however.

In an NBC News/Wall Street Journal poll this week, 69% of respondents said they agreed with Barbara Bush’s January comment that there should be “more than two or three families” that seek high office.

George W Bush said his brother is “checking his core” and thinking about potential impact on his family before he makes his decision.

But if Jeb needs a compassionate ear, Bush had a suggestion: “Hey Jeb, if you need some advice, give me a call.”