Trump has appointed Christie the chairman of a "Transition Team" to help "take over the White House when we win in November."
Trump's campaign announced the news via a statement which read: "Governor Chris Christie will serve as Transition Team Chairman, overseeing an extensive team of professionals preparing to take over the White House, and all that entails, in the fall. Governor Christie has been a loyal supporter and confidant to Mr. Trump and the campaign."
The governor, who drew widespread scrutiny for his early decision to back Trump, told Jimmy Fallon last month that he "has a hard time believing anyone would ask me to be vice president" – but he didn't rule out the possibility of sharing a ticket with Trump.
The New York Times recently reported that sources close to Christie said he was willing to consider being Trump's running mate, but when asked about it at a Statehouse news conference Monday, Christie replied, "As I've said all along, one, I don't think I'm going to be asked. Two, I don't know that I'm necessarily the right person for it."
"Three, you never say never to anything in this business, because you don't know how you're going to feel if you get approached about anything," he added, according to Philly.com. "That's about any future job in a Trump administration."
Several other politicians have raised their hands to express interest in the job – albeit a little reluctantly.
Former Arizona Gov. Jan Brewer said Sunday that she would be "willing" to serve as Trump's vice president.
"Of course I would be … willing to serve in any capacity that I could be of help with Donald on," Brewer told Jake Tapper on CNN's State of the Union Sunday, after viewing a short-list that included Marco Rubio, former U.S. Secretary of State Condoleezza Rice, Oklahoma Gov. Mary Fallin and former Speaker of the House Newt Gingrich.
"But that's a tremendous list of people to choose from," she added. "They're all very wonderful people, well-qualified. I certainly think that Newt, I've known him for a long time, we all have experienced what he can get done in Washington, D.C. And Marco Rubio would be terrific. Mary Fallin would be terrific."
Gingrich told The Wall Street Journal Thursday that he "might" be willing to serve as Trump's running mate, though he did not elaborate on his interest. Gingrich previously told The New York Times, "If a potential president says I need you, it would be very hard for a patriotic citizen to say no. People can criticize a nominee, but ultimately there are very few examples of people turning down the vice presidency."
Former Texas Gov. Rick Perry officially endorsed the billionaire businessman as "the people's choice" on Friday and said he would be open to being Trump's running mate.
"I am going to be open to any way I can help. I am not going to say no," Perry told CNN of potentially becoming the Republican vice presidential nominee. "We can't afford the policies and the character of Hillary Clinton."
"He is not a perfect man. But what I do believe is that he loves this country and he will surround himself with capable, experienced people and he will listen to them," Perry also said of Trump. "He wasn't my first choice, wasn't my second choice, but he is the people's choice." Maine Gov. Paul LePage said Wednesday he is considering running for Senate in 2018, "if I'm not into the Trump administration."
Marco Rubio, Ben Carson and Others Who Have Said 'No' to Being Trump's Running MateBut for every door left open to being Trump's vice presidential pick, another door closes.
Former GOP hopeful Rubio sparked interest in a potential Trump-Rubio ticket when he praised the businessman last week by saying his "performance has improved significantly." But a Rubio adviser tells PEOPLE, "He was never interested" in being Trump's running mate.
Former New York City Mayor Rudy Giuliani and others have suggested former Secretary of State Condoleezza Rice, now a professor at Stanford University, as a potential vice president for Trump. But her chief of staff, Georgia Godfrey, tells PEOPLE, "She is not interested. She's happy at Stanford and plans to stay."
Ben Carson – a former GOP hopeful who Trump has said will be on a committee to select his running mate – said he's "not interested" in the job himself "for a number of reasons." "I don't want to be a distraction," he told The Wall Street Journal.
On Thursday the campaign manager of Ohio Sen. Rob Portman said he wouldn't consider being Trump's running mate. "It's not happening, period."
And South Carolina Gov. Nikki Haley said Wednesday that she would support Trump in the general election but added that she is "not interested in serving as vice president," Politico reports.
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Florida Gov. Rick Scott, who hails from an electorally crucial state, has been tossed out by The Washington Post as a possible running mate for Trump. Scott has been early and vocal in his support for Trump, even taking to Facebook before the real estate mogul clinched the nomination to urge Republicans to unite behind Trump.
But Scott too said he would decline to be Trump's vice presidential candidate, Politico reports. "I like my job. I worked hard to get this job. I'm going to stay in this job," Scott said on CNN's Erin Burnett Outfront.
New Mexico Gov. Susana Martinez is another politician whose name has cropped up as a suggested contender for Trump's vice president, but a spokesperson for Martinez told The Weekly Standard Thursday that, "The governor has said repeatedly over the years that she isn’t interested in serving as vice president. She appreciates that such attention puts New Mexico in the spotlight, but she is fully committed to serving the people of our state."
Who Does Donald Trump Want to Be His Vice President?Trump said Thursday there is "probably a 40 percent chance" he would pick one of his 16 former GOP presidential rivals, but added that he was "unlikely" to choose Ohio Gov. John Kasich.
Some commentators have pointed out the obvious: Trump, given his sizable polling deficit with women, might do well to choose a woman running mate. One of his most notable endorsers, former Alaska Gov. Sarah Palin, has 40/1 odds on getting the position, according to Paddy Power.
In a Good Morning America interview Wednesday he said his vice presidential pick would definitely be a Republican and would "most likely" be an elected official.
Trump said Thursday that he will announce his vice presidential pick at the GOP convention in July.