The Republican Vice Presidential Nominee says he believes Holcomb could best do the job.
Pence tapped Holcomb to be the Hoosier State’s Lieutenant Governor earlier this year.
Representative Susan Brooks, Todd Rokita, and Senator Jim Tomes have also submitted their name for consideration.
The Republicans must caucus and pick their candidate in the next few weeks before squaring off against Democrat John Gregg in November.
U.S. Senate Candidate Evan Bayh Visits Evansville
Bayh believes he is the man who can help Republicans and Democrats work together.
He pointed to his long track record of being governor and U.S. Senator as why people prefer him to Baron Hill, who dropped out of the race last week.
Bayh said if he wins, he will work to create jobs, cut taxes, grow small businesses, and make college more affordable. He also stopped in South Bend, Gary, and Terre Haute.