"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.
Hillary Rodham Clinton, center, along with former Secretary of State Madeleine Albright, right, and Annette Tilleman-Dick, left, wife for former Rep. Tom Lanots, D-Calif. Clinton was honored with the Tom Lantos Human Rights Prize during a ceremony last week at the Cannon House Office Building. Previous winners include the Dalai Lama and Elie Wiesel.
Each year since 1990, CQ Roll Call has reviewed the financial disclosures of all 541 senators, representatives and delegates to determine the 50 richest members of Congress. This year's report, derived from forms covering the calendar year 2012, shows it took a net worth of $6.67 million to crack the exclusive club.