The 19-year-old is already an important player for the Austrian side, with his great form leading to interest from across Europe.
But Napoli have now entered the race and held initial talks with Salzburg to explore a deal.
The Azzurri faced Salzburg in the Champions League this season and relations between the clubs are excellent.
Napoli have the multi-talented midfielder is in their sights and could make a formal offer in the coming weeks.
Hungary midfielder Szoboszlai has made 19 appearances in the Austrian Bundesliga this season, registering an impressive seven assists.