Stewart said: "I did email her [Elton] and said: 'What, again dear'? And I didn't hear anything back.
"Talking about retirement, I've never spoken about retirement, and if I do retire, I won't make an announcement. I'll just fade away. I don't think this big deal: 'I'm going to retire', it stinks of selling tickets."
When Cyndi Lauper, who is touring with Stewart and also appeared on the show, joked that it "wasn't a bad idea" and that they too could plug their tour in the same way, Stewart said: "It's dishonest. It's not rock and roll."
Stewart and Elton have enjoyed a good natured rivalry for years and have in the past texted each other to compare album sales. During their conversations they pretend to be a married couple and Stewart calls himself Phyllis while Elton is Sharon.