The 20-year-old Hungarian talent is on the wish list of some of the biggest outfits in Europe and is expected to depart Red Bull Salzburg in January.
He has a €25m exit clause, which expires in the middle of next month and teams are expected to trigger that with a view to a move in the winter market.
Arsenal are reported to have already put in legwork on a deal, and Dominik has also been linked with a transfer to AC Milan, Inter Milan, Juventus, Napoli, Paris Saint-Germain, Bayern Munich and Real Madrid.
But it has been stated that RB Leipzig are the ones who are in pole position to snap up the Hungarian in the winter transfer window.
RB Salzburg are their sister club and they think that they will be able to get a deal done to land him in the coming month.
Konrad Laimer, Dayot Upamecano, Naby Keita and most recently Hwang Hee-Chan have all moved from Salzburg to Leipzig in the latest years.
And the German club believe that Dominik will become the next talented youngster to cross the Red Bull bridge in the next window.
In other news, Arsenal will allegedly look to offload Nicolas Pepe in January if the club can find a suitable buyer for the attacker.
The Ivory Coast international has performed relatively well in the UEFA Europa League this season, but his struggles in the Premier League have been well-documented since his arrival from the Ligue 1 side Lille last summer.