Gross has shone at Brighton & Hove Albion in the Premier League and helped Graham Potter’s side to avoid being dragged into the drop zone last term.
He made 34 appearances in the Premier League last season and chipped in with eight assists, along with scoring three goals for the Seagulls.
The German’s performances have seen him linked with Jurgen Klopp’s Liverpool, but he is, according to Italian outlet Tutto Mercato, fascinated by Italy’s Serie A.
And the midfielder is attracted by the idea of moving to Serie A in the future.
It is claimed that Gross already has interest from Italy, but it remains to be seen if any of his suitors choose to firm up their admiration with a bid.
Brighton snapped Gross up from German side Ingolstadt in the summer of 2017, shelling out £3m to secure his services.
The Seagulls have Gross under contract until the summer of 2022.