President Obama's Secret Mission ... 'Jimmy Kimmel Live'

2:15 PM PDT -- A rep for the Kimmel show tells TMZ Obama will not be doing the show Wednesday. Our ABC sources, however, continue to say he was booked on the show and multiple LAPD sources continue to tell us Obama is scheduled to be at The El Capitan Wednesday at 3 PM for an hour.

President Obama is juggling at least two world crises, but it's not cramping his pop culture style -- we've learned he's coming to L.A. this week to appear on Jimmy Kimmel's show.

ABC Network sources tell TMZ ... the Prez will come to Kimmel's studio Wednesday to tape a special segment. We're also told a big chunk of the interview will be "serious."

The show is shot at the legendary El Capitan theatre on Hollywood Blvd.

LAPD sources tell TMZ ... the President will only be at in Hollywood for an hour -- at the El Capitan -- beginning at around 3 PM.

We're told the Secret Service has been all over the El Capitan in the last few days.