The Cherries secured a first-ever European qualification at the end of last season under former boss Andoni Iraola and the club subsequently rejected several offers for the England international in the summer.
Chelsea were heavily linked with a formal bid and Iraola also hinted at an interest in bringing him to Anfield.
Scott is under contract at Bournemouth until 2028, but the 23-year-old has not entered extension talks at this stage, but the Cherries remain hopeful they can convince him over their long-term project.
Keeping Scott at the Vitality Stadium is Bournemouth's objective, but they are unlikely to drag contract talks on beyond the start of 2027 if he resists a renewal, and Real Madrid are ready to rival Chelsea in a £70M bidding war.