The pair recently rubbed shoulders on the front row at the Chanel show for Paris Fashion Week and 22-year-old Giabiconi has apparently had his eyes on Perry for the last 14 months.
Giabiconi is the face of the French fashion house and reportedly the highest-paid model in the world. He is quoted by The Sun as saying a year ago: "If I could make her (Katy Perry) divorce her husband, I'd marry her."
The rumoured couple were apparently spotted leaving a five-star hotel in the Fashion capital together, with an onlooker adding to the tabloid: "They were with a group of people, but they looked very much like a couple in love. He was never more than a foot away from her and they were very flirty.
"There was a lot of whispering, shared jokes and they were really flirting."
Perry and 36-year-old Russell Brand, who has been romantically linked to Mexican make-up artist Oriela Medellin Amieiro, announced the end of their 14-month marriage last year.