The Hungary captain has a £60million release clause in his contract which has been triggered by the Reds.
The two clubs are still negotiating the make up of the deal, with Liverpool keen to pay the fee in installments.
Sources have told talkSPORT Newcastle are not competing with Liverpool for Szoboszlai, despite reports the Magpies were also tracking him.
Szoboszlai made 46 appearances for RB Leipzig last season as they finished third in the Bundesliga, just four points off champions Bayern Munich.
The midfielder scored 10 goals in all competitions whilst also providing 13 assists.
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News of the breakthrough will be a big boost to Jurgen Klopp's side as they look to get prepared for the upcoming season.
Alexis Mac Allister has already joined the club from Brighton with the Reds allowing James Milner to go the other way.
They also allowed young midfielder Fabio Carvalho to join RB Leipzig on loan for the upcoming season.