Speaking to US chat show host Andy Cohen on Bravo TV, Sir Rod said he did not believe in retirement tours.
"I've never spoken about it and if I do retire, I won't make an announcement. I'll just fade away," he said, adding that retirement tours were "dishonest".
Sir Elton, who announced his farewell tour in February, hasn't responded.
Sir Rod was responding to a question from a caller on Cohen's Watch What Happens Live, asking what he thought about his fellow pop legend's tour.