The 23-year-old left-back has left Hull’s pre-season training camp in Portugal in order to have a medical with the Reds on Thursday.
The deal is expected to be £8 million ($10.4 million, 9 million euros) up front, followed by £2 million in add-ons.
Robertson has been instrumental for the Tigers since arriving from Dundee United in 2014 in a £2.8 million deal, making 112 appearances for the East Yorkshire outfit.
Robertson, who has 15 Scotland caps, will become Liverpool boss Jurgen Klopp’s third summer signing, following the arrivals of Dominic Solanke and Mohamed Salah.
Earlier on Wednesday, the East Yorkshire side announced the sale of goalkeeper Eldin Jakupovic to Leicester City for an undisclosed fee.
