Salazar, a former state attorney general, had been considered a leading contender to replace Democratic Gov. Bill Ritter, who announced Wednesday that he will not seek a second term.
The Post report says that Salazar has endorsed Denver mayor John Hickenlooper for the job.
""John Hickenlooper is a uniter," Salazar told the Post. "He brings people together. He can bring business and labor together."
Hickenlooper has said that he is considering a run for the state's top job.
Salazar was one of Colorado's U.S. senators between Jan. 2005 and Jan. 2009, when he resigned to take a cabinet position in the administration of President Barack Obama.
Obama had given Salazar his approval for a decision to leave the administration to return home for a gubernatorial run.