The actor has been looking to get away from it all since Katie Holmes, 33, filed for divorce in June.
He’d been considering staying in the medieval Castle Of Lions – which is located 100 miles north of Rome – but George, 51, wants him to consider Villa Oleandra.
If Tom, 50, takes George up on his offer, he won’t be the first A-lister who’ll have enjoyed the waterfront house.
In 2010, Emily Blunt chose it as her wedding venue while Angelina Jolie, U2‘s Bono and Cindy Crawford have all spent time there.
Tom is also rumoured be looking at places to live in New York, where his 6-year-old daughter Suri lives with mum Katie.