Former Florida Governor Jeb Bush has made a leap in his campaign run for the White House, leading the list of Republican presidential contenders in at least two national polls released this month.

The Hill, a top US political newspaper read by the White House and more lawmakers than any competitor, reported that Bush now has a clear lead in polling both nationally and in New Hampshire, improving his chances to be the GOP nominee.

"He runs 7 percentage points ahead of his nearest rival in CNN's latest national poll and beats the field in New Hampshire by about 5 percentage points, according to the RealClearPolitics (RCP) average," The Hill said on Monday.

Wisconsin Gov. Scott Walker, a favorite in Iowa, trails behind at second place since his 17.5 percent support in RCP average helped him occupy the position as the main conservative challenger to Bush's 19 percent, The Hill said.

The non-partisan American political publication explained that one of Bush's advantages is that he is expected to have "truckloads of cash" that is needed to sustain a long campaign and help him in March.

Eleven states are scheduled to vote on Super Tuesday, March 1.

"If the race is still competitive by March 15, Bush's money edge will be augmented by home-court advantage when Florida votes, along with Illinois, Missouri and Oregon," The Hill said.

But despite Bush's national strength, The Hill said Bush is highly unlikely to win the Iowa caucuses, where he places sixth in the latest major poll held there.

The Hill made the reveal in its latest list titled "The 10 Republicans most likely to win the GOP's 2016 nod" published on Monday or a month before the first GOP presidential debate is set to be organised.

A new CNN national poll also agreed that the son and brother of two former American presidents is on top of the list of GOP presidential hopefuls, holding a double-digit support among Republicans and GOP-leaning independents.

In a report published on July 1, CNN Polls said Bush stands at 19 percent, which is 7 percent higher than the 13 percent he was at in May—his best showing in CNN/ORC polling so far.

"The findings suggest Bush is making progress toward being seen as the frontrunner in a field that has long lacked a clear leader," CNN Polls said.

But the same poll noted that the former Florida governor is actually sharing the top spots with real estate mogul Donald Trump, who follows with 12 percent, with an improvement of 3 percent before he made his campaign announcement.

"He (Bush) holds a significant lead over the second-place candidate Trump, is seen as the candidate who could best handle illegal immigration and social issues, and runs about even with Trump and well ahead of the other candidates when Republicans are asked which candidate can best handle the economy," it added.

Unranked in May, Trump occupies the eighth spot in The Hill's national poll.