REUTERS/John Sommers II
Donald Trump (R) and Indiana Governor Mike Pence (L) wave to the crowd before addressing the crowd during a campaign stop at the Grand Park Events Center in Westfield, Indiana, July 12, 2016.
CBS News also confirmed the news with a source.
The Times noted that Republicans caution Trump could still change his mind. Several sources told the Times that Trump is preparing the announcement with Pence, which is expected to come on Friday morning.
Pence is a former congressman who has been called a "rising star" among conservatives. He chose to run for governor of Indiana in 2012 rather than seek the Republican nomination for president.
Trump has been meeting with prospective running mates this week ahead of the Republican National Convention in Cleveland next week.
Roll Call cited an unnamed Republican "with direct knowledge of the situation" who says Pence will be the vice presidential pick.
Pence beat out New Jersey Gov. Chris Christie, former Pennsylvania congressman Newt Gingrich, and several others.