The Cherries secured a first-ever European qualification at the back 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 lingering 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, despite the Cherries ongoing confidence they can convince him to sign a deal.
If Bournemouth admit defeat in their attempts to keep the former Bristol City man, they were rumoured to have set a £100M asking price, based on Elliot Anderson and Enzo Fernandez both moving for over that figure in August.
However, as Chelsea continue to work on a deal, there's growing confidence from Stamford Bridge over landing an agreement for closer to £90M.