"I'd like to think, yes, we would," Starr told The Mirror. "Paul still goes out with his band, I go out with mine and John would have probably been going out with his."
He added that George was never big on touring so wasn't sure if he would have been up for it, but said: "But who knows... it could have come together."
John Lennon was 40 years old when he was shot dead by Mark David Chapman outside his apartment building in New York on December 8 1980. George Harrison died from cancer in November 2001 aged 58.
Ringo, 72, and Sir Paul McCartney, 70, are the only surviving members of the band, and actually did reunite with Harrison after Lennon died to add some of the late singer's vocals to the songs Free as a Bird for 1995's Anthology 1 and Real Love for 1996's Anthology 2.
Ringo, real name Richard Starkey, is currently promoting his new e-book Photograph, which is released this week and features rare photos - many published for the first time - of a behind-the-scenes glimpse of life as a Beatle.
Many of the snaps were taken from cars or in hotel rooms and speaking to Today, he said: "We lived from gig to car to hotel room.
"When we got to New York - when we got to America - it was, like, too big, because all the music we loved came from America. It was like a dream come true."
The Beatles formed in Liverpool in 1960 and worked and played hard to achieve their global status. Something which Ringo believes cannot be achieved by reality TV shows.
He said: "I may sound like an old fart, but you win a TV show, but you haven’t put in your time."