The Anfield club have sent a scout to Poland to watch the 18-year-old play for Germany's Under-19s this week.
And Havertz did not disappoint as he scored four goals and assisted another in a 5-1 win over Belorussia's Under-19s in Zabrze.
Described in Germany as '50 per cent Michael Ballack, 50 per cent Mesut Ozil', he is regarded as the top talent of his age-group and a number of European clubs are currently following him closely.
But Liverpool appear to be near the front of the queue for his services with Jurgen Klopp's presence at Anfield a potential decisive factor should he move abroad.
Leverkusen will hope to hold onto him for as long as possible but will be reluctant to sell the youngster to a rival Bundesliga club when the time comes.
In June, it was reported that Liverpool had spoken to Leverkusen about the avilaibility of havertz and full-back Benjamin Henrichs.