The pair were spotted enjoying an evening together at a posh London nightclub earlier this month.
The teenager tried to win over the self-dubbed "blonde assassin", telling her: "You're the fittest Apprentice bird I've seen. I hope you win."
But married Katie snubbed his advances.
"Frankie's not exactly her type," a pal revealed.
Still, it didn't stop the 26-year-old from enjoying a night of vodka shots with the singer as the pair were pictured rather drunk falling out of the club together come the early hours.
[cat]The Apprentice[/cat] continues on BBC One tonight.