The Times is reporting that the Reds have reached an agreement with the Tigers that could see the fee increase to £10m due to add-ons.
The same article states that Robertson will undergo his medical at the Merseyside club on Thursday ahead of a move to the 18-time English champions.
According to the same story, Jurgen Klopp wants to sign Robertson to provide retired England international James Milner with competition at left-back.
The Times claims that the Liverpool boss had previously looked at the possibility of signing AS Monaco defender Benjamin Mendy and Fulham teenager Ryan Sessegnon.
Liverpool have already signed England Under-20 international Dominic Solanke in a free transfer and AS Roma winger Mohamed Salah in a club-record £36.7m deal earlier this month.
Klopp led Liverpool to a fourth-place finish in his first full season in charge at Anfield but the German coach is still waiting to lift his first trophy since taking over the reins in 2015.
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