The 20-year-old Hungarian midfielder is on the wish list of some of the biggest clubs in Europe and is expected to leave Red Bull Salzburg in January.
He has a €25m release clause, which expires in the middle of next month and clubs are expected to trigger that with a view to a move in the winter window.
Arsenal are claimed to have already put in legwork on a deal, and he has also been linked with a move to AC Milan, Inter, Juventus, Napoli, Real Madrid, Bayern Munich and Paris Saint-Germain.
But it has been claimed that RB Leipzig are the ones who are in pole position to snatch the Hungarian in the winter transfer window.
Red Bull Salzburg are their sister club and they believe that they will be able to get a deal done to sign him in the coming month.
Naby Keita, Dayot Upamecano, Konrad Laimer and most recently Hwang Hee-Chan have all moved from Salzburg to Leipzig in recent years.
And the German club believe that Szoboszlai will become the next talented prospect to cross the Red Bull bridge in the next window.