"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.
James Jones, communications director for DC Vote, tapes a "DC Constituents Service Day" sign on the wall as he stands with other DC residents outside of Rep. Andy Harris's office on Capitol Hill to protest Harris' actions against D.C.'s marijuana laws on Thursday, July 24, 2014. DC Vote encouraged DC residents to bring their complaints about city services to the Maryland congressman.