Andrew Robertson will undergo a medical on Thursday ahead of his move from Hull to Liverpool, according to Sky sources.
The Scotland left-back flew back from the Tigers' pre-season tour in Portugal earlier this week after a £10m fee between the clubs had been agreed.
Sky Sports News understands several other Premier League clubs were also interested in signing Robertson along with PSV Eindhoven and Sporting Lisbon.
Robertson made 39 appearances in all competitions last season, but was unable to prevent Hull from suffering relegation from the Premier League.
If the 23-year-old passes a medical and agrees personal terms, he would become manager Jurgen Klopp's third signing of the summer following the arrivals of Mohamed Salah and Dominic Solanke.
Robertson started his career at Queen's Park before moving to Dundee United and then to Hull in July 2014.
Sky Sports News also understands Hull have agreed a fee with Liverpool for midfielder Kevin Stewart.
Stewart has been given permission to fly back from Liverpool's Asia tour to begin talks with the Sky Bet Championship club.
His potential move to the KCOM Stadium is not part of the deal to take Robertson to Anfield.