Bob CorkerBob CorkerFinal frenzy in Trump VP search Buzz builds around Pence for Trump's VP Sunday shows preview: Week's violence inflames the country MORE of Tennessee, took himself out of the running.
New Jersey Governor Chris Christie is among the candidates being considered.
Get to know those three potential veeps below.
Trump knows Pence less personally than Gingrich and Christie, who have been vital behind-the-scenes advisers to the candidate. That's according to a person familiar with Trump's thinking, who spoke on condition of anonymity because the person was not authorized to discuss the vetting process.
The billionaire businessman has provided a few clues about what he's looking for in a No. 2, telling the Wall Street Journal he needs an "attack dog" and a "fighter skilled in hand-to-hand combat".
Mr Trump, the likely nominee, and his children were seen leaving the Pence home in Indianapolis. Jeff Sessions and former House speaker Newt Gingrich.
Anti-Trump delegates are expected to make one last play on Thursday: a request to the convention rules committee for a change that would allow delegates to vote for any candidate next week, regardless of whether or not they are bound to Trump.
Trump, his adult children and key staffers huddled with one of the prospects, Indiana Gov. Mike Pence, Wednesday morning at the governor's mansion, a day after the pair campaigned together in the state.
Pence (R) and his wife, Karen, stood outside their front door and waved goodbye to Trump as his motorcade pulled out of the governor's driveway about 10:30 a.m.
Trump was joined early Wednesday by his eldest daughter, Ivanka, and her husband, Jared Kushner; his sons Donald Jr. and Eric; and some advisers, including campaign chairman Paul Manafort. The Indiana governor's decades of political experience and his reputation as a staunch social conservative make him an appealing choice for Trump, who has struggled to win over segments of both the hard right and the Republican establishment. Gingrich is a boisterous rabble-rouser who has spent decades in Washington, including as House speaker.
Christie has become a close advisor to Trump ever since he dropped out of the presidential race and endorsed him. He's also met with the candidates and brought his finalists on tour to test their receptions before his crowds.
Trump stayed in the state after campaigning with Gov. Mike Pence Tuesday night.
Although Pence, a former congressman and talk radio host, endorsed Texas Sen.
At Tuesday's rally, Pence slammed Clinton, saying that "to paraphrase the director of the Federal Bureau of Investigation, I think it would be "extremely careless" to elect Hillary Clinton as president".
In an interview with The Associated Press on Monday, Trump said he'd narrowed his list to four contenders.
Trump tells Fox News channel he's getting closer to his decision. "Because Trump has never held office and people are anxious to see how he would assemble a government, this pick might get more attention than usual", said Republican strategist Charlie Black.
Still, Trump left the vice president question unanswered during his speech in Indianapolis Tuesday.