"We have looked at this thing from every which way," Thomas told the insider newsletter. "It doesn't make sense to get in. We don't see a chance to win. I don't want to be a second candidate against an incumbent."
His decision means Mourdock will likely have a clear shot against Lugar in the May primary. The state filing deadline is Feb. 21.
Thomas also said he would not endorse Lugar or Mourdock.
In 2010, Thomas spent $600,000 out of his own pocket to challenge then-Rep. Mark Souder (R-Ind.). Thomas lost his primary bid to Souder by about 14 points in what was a crowded GOP field.
Former Sen. Scott Brown, R-Mass., candidate for U.S. Senate in New Hampshire, holds his hand over his heart during the singing of the national anthem as he waits to take the stage for his town hall campaign rally with Sen. John McCain at the Pinkerton Academy in Derry, N.H., on Monday, Aug. 18, 2014.