The Cherries sealed a first-ever European qualification at the end of last season, under former boss Andoni Iraola, which allowed the club to reject several offers for the England international over the summer.
Chelsea were heavily linked with a formal bid and Iraola also hinted at his interest in bringing him to Anfield.
Scott is contracted to Bournemouth until 2028, but the 23-year-old has not entered extension talks at this stage, with the Cherries still holding out hope they can convince him over a deal.
Real Madrid and Chelsea have both been linked with £70M bids - but Iraola could trump both clubs - as the Reds appear ready to offer closer to £100M and he could be paired with another new arrival on Merseyside in Lamine Camara.
The pair's strong relatoinship is also a big bonus for Liverpool and that could sway Scott on his final decision.