The comedian, 68, met Smiley in New York, according to The Mirror.
Smiley then apparently joined Cleese and movie director Michael Winner on a European holiday around Switzerland and Italy.
"She's definitely a girlfriend," said Winner.
Cleese commented: "She's certainly a new friend. More than that, I simply don't want to disclose because the relationship is in its early stages."
The Fawlty Towers star is currently undergoing a divorce from his third wife Alyce Faye Eichelberger.