The answer to the “Jeopardy” clue “Alex Trebrek’s replacement” has a new and surprising question:

“Who is Matt Lauer?”

The beleaguered host of the “Today” show is at the top of the list to take over the brainy game show when Trebek steps down, as expected, in 2016, knowledgeable sources tell The Post.

Lauer is widely reported to be on his way out at the morning show, which has tumbled to No. 2 in the ratings in the last year. He is being blamed for the show’s fall from grace after 16 years on top.

The Post reported this week that Lauer is not expected to re-sign with “Today” when his blockbuster, $25-million-a-year deal expires in 2015.

By coincidence, that’s about the time Trebek is expected to end his three-decade run as the host of the habit-forming game show.

Sony Pictures Television, which owns the hugely profitable show, has quietly been feeling out TV personalities in recent months to see who might be available and willing to take on the role in 2016, sources say.

Trebek — who suffered his second heart attack last summer — said in interviews last year that he was thinking about retiring this season.

But Sony convinced him to sign one final, three-year contract — taking him to age 76 — to give producers enough time to find a next-generation successor.

Trebek is so thoroughly identified with “Jeopardy” that finding a new face for the show is a decision that will take several years to make.

According to sources with knowledge of the internal discussions, Sony is also strongly considering Anderson Cooper — whose contract with CNN reportedly ends next year — for the job.

But right now, Lauer’s name is at the top of the list, several sources say.

Until this week, Sony thought it might have to convince Lauer to do double duty on a game show and the morning show.

But if Lauer is off “Today,” it makes him suddenly available.

It is unclear if Sony has approached Lauer’s long-time agent, Ken Lindner.

But one source says that Cooper — who hosted a competitive reality show on ABC called “The Mole” before his CNN days — knows that “Jeopardy” wants to talk and “he likes the idea.”

Hosting a show like “Jeopardy” is not nearly as time-consuming as a daily show like “Today.”

Meredith Vieira hosted “Who Wants to Be a Millionaire” during all five years she was on “Today” with Lauer.

In fact, game shows can tape a week’s worth of shows in a single day and some shows — like “Millionaire” — can shoot nearly a whole season in seven or eight weeks.

Final decisions on all these moves are at least a year-and-a-half away, and much can happen before then.

“In this business,” said one insider with knowledge of the players, “that’s a lifetime.”

Calls to Lauer’s agent yesterday were not returned.

A spokesman for “Jeopardy” declined to comment.