06/14/2012 11:48 am ET

Jimmy Fallon: 'Tonight Show' No Holy Grail, He Tells Piers Morgan (VIDEO)

On Wednesday's "Piers Morgan Tonight," guest Jimmy Fallon told the CNN host that he has no aims to leave his "Late Night" perch to take over the "Tonight Show," no matter how prestigious the latter show may seem.

"There is a growing buzz around town that maybe it's time you were on a little earlier on NBC," Morgan said to Fallon. "Like 11:30," he said, referring to the timeslot of the "Tonight Show."

"That buzz isn't coming from me," Fallon replied without hesitation. "I like being where I am."

Of course, that's the only reasonable answer Fallon could possibly give. His incarnation of "Late Night" has only been on the air for just over three years. His predecessor, Conan O'Brien, had a 17-year audition to prove he was worthy of taking over the "Tonight Show," but NBC executives changed their minds only seven months (and millions of dollars) into O'Brien's run at 11:30 in 2010.

After O'Brien left NBC's airwaves, Fallon made light of "Late Night" hosts' luck in moving to the earlier timeslot. "There have been three hosts of 'Late Night': David Letterman, Conan O'Brien, and me," he said at the time. "And if there's one thing I've learned from Dave and Conan, it's that hosting this show is a one-way ticket to not hosting the 'Tonight Show.'"

But the reality is that Jay Leno is 62 years old, and cannot feasibly host the show too far into the future. Would Fallon turn down the job if it were offered? "No, I wouldn't turn it down," he said.

"Is it the Holy Grail?" Morgan asked.

"No," Fallon replied. He voiced the opinion that no "Tonight Show" host will ever replace Johnny Carson, and that while the franchise continues to have the same name, audiences primarily identify with the man behind the desk.

"Timeslots don't matter to me, especially that late at night. You just do your show and and work hard and keep your head down, and have fun with it," Fallon said.

Fallon's newest music album, a collection of songs from "Late Night" entitled "Blow Your Pants Off," hit stores this week.