The 26-year-old singer has become interested in dating Giovanni, of Plaka, while she oversees the creation of a USD 10 million palace in Crete, reported Daily Star.
"Gaga is very taken with Giovanni. He is a fast-talking Romeo with his own business, and she can't seem to keep away from him. They got to know each other when she started eating in his restaurant on a regular basis," a source said.
Gaga talks to the businessman regularly despite her hectic schedule.
"Everyone started saying they were lovers, which he hasn't denied. But he admits they are close and speak to each other most days," the source added.
Giovanni has allegedly been teaching the 'Poker face' hitmaker how to speak Greek.
R&B star Rihanna and rapper Drake are leading the MTV Video Music Awards (VMA) nominations with five nods each.