The 20-year-old Hungarian has attracted the interest of some of the biggest clubs in Europe and is almost certain to leave Red Bull Salzburg in the near future.
Arsenal have held talks with his representatives, with Real Madrid and Paris Saint-Germain also believed to interested in securing his services when he does move on from Austria.
AC Milan, Inter, Juventus and Napoli are all also in the hunt and the midfielder could consider a move in the January transfer window, which is now rapidly approaching.
And according to Italian outlet Calciomercato.it, the player will take a decision on his future at Red Bull Salzburg following the end of the Champions League group stage.
Red Bull Salzburg will play Bayern Munich, Lokomotiv Moscow and Atletico Madrid in the last three games of the Champions League group stage.
The Austrian outfit would prefer to sell him in the summer, but there is an increasing likelihood that the player could consider leaving in January.
A move in the middle of the season could hand the advantage to RB Leipzig, where Julien Nagelsmann is prepared to sign him in January.
Szoboszlai is available for a fee of €25m due to a release clause in his contract with Salzburg.