Among the possible picks are former US House of Representatives Speaker Newt Gingrich, Indiana Governor Mike Pence, New Jersey Governor Chris Christie and retired Lieutenant General Michael Flynn, according to media reports and Republican sources.
"I have it down to five people," Trump told Fox News on Tuesday.
Pence introduced Trump at a campaign rally in Westfield, Indiana, on Tuesday evening. "I don't know if he's going to be your governor or your vice president. Who the hell knows," Trump told the rally.
Gingrich and Christie have also campaigned with Trump in recent weeks.
The Republican National Convention, where Trump is set to be formally nominated as the party's candidate for the Nov. 8 election, begins on Monday in Cleveland.