They together had a string of dinner dates together and that has set the tongues wagging.
Campbell and the 61-year-old have reportedly been working to keep their romance secret — utilising private jets to meet up.
“Naomi and Louis have been secretly dating for weeks. They’re all over each other when they’re out,” the source told The Sun newspaper.
“Naomi likes to keep her relationships private and it is early days but there’s a real spark between them and their close friends are aware they’re dating,” the source added.
Camilleri is chairman of Philip Morris International — a global cigarette and tobacco company.