The wealthy businessman, a political neophyte, has said he wants a political veteran to help him navigate the power corridors of Washington.Gingrich and Christie, both loyal to Trump at a time when many Republican colleagues want nothing to do with him, would meet his requirement for experience - but would come with minuses as well as pluses.
Other names included notably recommended Senator Bob Corker of Tennessee and governors Mike Pence (Indiana) and Mary Fallin (Oklahoma). Pence can not serve as Trump's running mate and run for re-election at the same time.
The newspaper said that Christie "is one of the few people who has the presumptive Republican presidential nominee's ear", and his reputation for fighting with the media, Democrats and other Republicans "will surely remind Trump of himself".
Republican Senators Lindsey Graham and John McCain said on CBS show "Face the Nation" that they would respect Attorney General Loretta Lynch's decision on whether to prosecute Clinton, the likely Democratic presidential nominee. He was Trump's biggest endorsement at a crucial moment in the campaign and that has sparked talk about any number of possible positions inside a Trump administration.
Clinton is expected to wait until after the Republican convention to announce her running mate, allowing her to use her pick to distract from any boost Trump receives from the GOP gathering.
In choosing either Christie and Gingrich, Trump would satisfy his desire for someone with political experience who could help him advance his legislative agenda through Congress.
"Only one person, Trump, is making the decision and he can change his mind from minute-to-minute", the source said. A source said Christie was instrumental in coaxing Trump to take a less confrontational stance with a Mexican-American federal judge overseeing a fraud case involving the candidate's now-defunct Trump University venture.
"I want to make it clear", Biden said.
"I cannot in good conscience vote for him", Talmage Pearce, a GOP delegate from Arizona's Fifth Congressional District, said in an interview.
"The people who are sick and exhausted of Washington - they don't want somebody who can manage the table better, they want somebody who will kick the table over", he said.
Under Pence, who has described himself as "a Christian, a conservative and a Republican, in that order", in has marched to the front lines of the nation's culture wars.
But with little more than two weeks before the start of the Republican National Convention, Mr Gingrich and Mr Christie have been asked to submit documents and are being cast as favourites for the post inside the campaign. His stock may have gone down, however, because he has not shied away from criticizing the candidate at times.
Biden then responded, "I think [Trump] needs the help, yes". Marco Rubio. Christie is the only one of the original five still on the list.
Barbour said that lack of discipline is part of why donors remain reluctant to give to his campaign, a reluctance that contributed to a shockingly low May haul that left Trump with just $1.3 million cash on hand. "He's the type of person who would bring a lot to the ticket".
"It's an honor to be mentioned for the office of vice president".
Would you be happy if Chris Christie ran with Donald Trump? .
Some Republicans could be considered even if they have not had recent contact with the campaign.