Scotland international Robertson, 23, will be the Reds' third summer signing.
Meanwhile, Liverpool's Kevin Stewart is set to join Hull in an £8m deal.
The midfielder, 23, has been allowed to leave the squad in Hong Kong, where Liverpool are competing in the Premier League Asia Trophy, to travel for talks with the Championship club.
In other transfer news, RB Leipzig's owner says the German club have rejected a 75m euro (£66m) bid for midfielder Naby Keita.
The 22-year-old Guinea international is another Liverpool transfer target.
Dietrich Mateschitz told German tabloid Bild: "We were flattered when an offer of 75m euros for Naby Keita recently landed at our door. No way. He still has a contract and he will fulfil it."
Keita, who scored eight goals and provided eight assists in his debut season for Leipzig after joining from Red Bull Salzburg last year, has a contract that runs until 2020.
However, there is a £48m release clause that can be unlocked next summer.
Since the end of last season, Jurgen Klopp's Liverpool have already completed the signing of winger Mohamed Salah from Roma for £34m, while England Under-20 forward Dominic Solanke joined after his Chelsea contract expired.
Brazilian midfielder Lucas Leiva was sold to Lazio for £5m on Monday.
Hull left-back Andy Robertson is to have a medical at Liverpool on Thursday after the clubs agreed an £8m deal that could rise to £10m.