Liverpool are scouting the Ghana international at the World Cup in Qatar ahead of making a potential move for him in January.
Sports World Ghana reports the Reds had scouts at the Black Stars' opening 3-2 defeat to Portugal, in which Kudus, who has previously admitted he 'loves the game' of Thiago Alcantara, marked his debut at the tournament with an assist.
Kudus has established himself as first-choice for Ajax under new manager Alfred Schreuder this season. He has scored an impressive 10 goals from 21 appearances in all competitions.
He also made an impact at Anfield as Ajax faced the Reds in the Champions League group-stages once again, scoring a thunderous equaliser in front of the Kop.