The 67-year-old television host first made overtures to Leno last year, according to TV Insider. The former Tonight Show host told the website he will "have to check into that" when asked about the guest spot.
Letterman and Leno are old rivals whose conflict stems from 1992. Letterman was passed over for Leno to replace Johnny Carson on The Tonight Show, leading the host to leave NBC and establish Late Show at CBS.
Leno went on to host The Tonight Show until 2009, when he was replaced by Conan O'Brien. He returned to the late night program in 2010, and continued to host until Jimmy Fallon took over the series in February 2014.
Letterman debuted Late Show in 1993, and announced his retirement in April 2014. His final episode will air May 20, with Stephen Colbert as his successor. The 50-year-old television personality hosted The Colbert Report on Comedy Central from 2005 to 2014.
"I'll tell you something, I can't wait for it to happen," Letterman said of his departure to Regis Philbin on The Late Late Show this week. "Because I am sick of tired of people saying, 'Well, what are you gonna do? What are you gonna do?' I have no idea what I'm gonna do."