Per Sky Sports News, the Reds have now made their move for the Scotland international, as manager Jurgen Klopp bids to strengthen his defence this summer, ahead of a Premier League title challenge.
Sky Sports reporter Kaveh Solhekol also added that Robertson has now flown home from Hull's pre-season tour of Portugal, suggesting a move to Merseyside is close:
Left-back has been something of a problem position for Liverpool, with Klopp having turned to the versatile James Milner as the club's first choice for most of last season, ahead of the erratic Alberto Moreno.
Robertson made 33 appearances for Hull City last season, as the Tigers were relegated from the Premier League after finishing in 18th place, but he will provide a solid option at left-back.
His displays have impressed the Reds, and Liverpool writer Jack Sear is confident in Klopp's judgement:
Per James Pearce at the Liverpool Echo, the arrival of Robertson could spell the end for Moreno, who could be allowed to leave Anfield after three years at the club.
Should Robertson arrive, he would become the club's third signing of the summer, following Dominic Solanke and Mohamed Salah to Anfield.
Liverpool are also being linked with further arrivals, including Red Bull Leipzig midfielder Naby Keita, although Pearce noted Klopp was refusing to be drawn on the club's ongoing pursuit of the 22-year-old:
Robertson, meanwhile, will help strengthen a Liverpool defence that conceded the most goals out of the Premier League's top four last season.
The Scot will also give Klopp further options, which will be needed to cope with the added demands of Champions League football on the squad.