Did David Letterman let something slip about his future on "The Late Show" Monday night?

Letterman sparked speculation around the TV business with a casual remark he made during an exchange with guest Albert Brooks, who was kidding Dave about this Friday being his last show ever.

"I don't think that's true," Letterman said.

"I think we are going to be here another two or three years."

Almost immediately, Dave-watchers were wondering if Letterman had made a backdoor announcement that he was thinking of retiring in two or three years. Letterman reportedly has nearly three years left on the "Late Show" deal he inked in 2002. That contract pays him a reported $31.5 million per year.

Letterman, 58, is notorious for keeping personal matters, such as contracts, close to the vest — which made the remark about his contract unusual, even if it was said in jest.

In three years, he will be 61.

It would also be 2009, the same year Jay Leno is scheduled to vacate his "Tonight Show" desk in favor of "Late Night" host Conan O'Brien.

For the record, Letterman's spokesman told The Post Tuesday: "Dave has no plans to retire."

Insiders say Letterman actually is "interested" in extending his deal with CBS beyond '09.

In fact, Letterman may have simply just opened contract negotiations with the suggestion he is thinking of retirement.

The whole thing began with a gag on Monday's show, when Brooks joked that he'd heard Friday would be Letterman's last show.

"I have had a knot in my stomach all day because obviously this will be the last David Letterman show I will ever do," Brooks said, adding that he heard the news about Letterman leaving from "the William Morris Agency."

After some banter, Brooks — parodying Bette Midler's serenading of Johnny Carson on his penultimate "Tonight Show" in 1992 — then sang to Letterman, while holding his hand, to the tune of "Thanks for the Memory."

Brooks made up funny lyrics about past news-making "Late Show" guests, including Drew Barrymore, who famously flashed Letterman on the air, and Farrah Fawcett, who seemed to have a meltdown on the show back in 1997.

Letterman signed the new deal in 2002 after threatening to jump to rival ABC when it looked as if that network was getting ready to cancel "Nightline" and enter the late-night comedy wars with CBS and NBC.

ABC ended up putting "Jimmy Kimmel Live" in the post-"Nightline" timeslot.