IF you catch her at the right moment, Janice Dickinson just might have sex with you for a sleeping pill.

The self-styled “World’s First Supermodel” was on a red-eye L.A.-N.Y. American Airlines flight the other night when she asked a fellow first class passenger how many cold pills she should take to put her to sleep for the rest of the flight. A handsome fellow seated nearby overheard and offered her a Xanax, a prescription anti-anxiety pill.

“I’ll [bleep] you in the bathroom for a Xanax!” Dickinson blurted.

The guy dead-panned, “I’ve got 10 of them,so I hope you ‘re not too tired.”

For the record,we’re told Janice took only one Xanax, fell asleep immediately, and performed no mile-high club hijinks.