Lucy Nicholson/Reuters
According to a show schedule tweeted out by New York Times reporter Dave Itzkoff, Musk is listed as one of the guests expected to appear on September 9.
The billionaire tech entrepreneur will be among some elite company.
Other celebrities and public figures on the list for Colbert's first week on the job include actor George Clooney, presidential candidate and former Florida governor Jeb Bush, actress Scarlett Johansson, author Stephen King, and comedian Amy Schumer.
Fellow tech entrepreneur Travis Kalanick will also make an appearance during the show's debut week. The Uber CEO is scheduled to be a guest on September 10.
Colbert was named as the new host of the "Late Show" after David Letterman decided to leave the program following 33 years at the helm.
The "Late Show with Stephen Colbert" will premier on September 8.