The 20-year-old attacking midfielder is on the wish list of some of the biggest clubs in Europe and he is being tipped to leave Red Bull Salzburg next month, due to the presence of a favourable release clause in his contract.
Arsenal and Tottenham are credited with holding an interest, while four Italian sides in AC Milan, Inter, Juventus and Napoli are also interested in the Hungary international.
RB Leipzig are on his tail as well and are reportedly the favourites to land the midfielder in the next two transfer windows.
But according to Italian daily Gazzetta dello Sport, the midfielder would prefer to join Serie A giants AC Milan as the next step in his career.
The Rossoneri have been interested in Szoboszlai since last summer and have been in constant touch with his entourage over a move.
And it seems the work has paid off and the player is believed to be keen on the move to the San Siro.
However, if they are to sign the midfielder in the winter window, the player will have to inform Red Bull Salzburg next week and AC Milan would have to trigger his €25m release clause by the end of the month.
A similar modus operandi would have to be followed if his suitors want to wait until the summer transfer window.
Any club signing him would also have to hand 20 per cent of any future transfer fee to Red Bull Salzburg as part of the deal.