Richter made the comments while he was filling in for Regis Philbin on Tuesday's "Live! with Regis and Kelly."
The sidekick acknowledged that a rumored live concert tour with O'Brien remains "a distinct possibility."
As for "The Tonight Show" job ending after just nine months, Richter was self-deprecating.
"I guess I'm really good at getting kicked off the air, because it's what I've been doing for the last 10 years," he joked.
Ripa joked back, "You and Conan could do another show on another network called 'We Were on The Tonight Show."