The Cherries secured a first-ever European qualification at the end of last season, under the guidance of former boss Andoni Iraola, which allowed the club to reject several bids for the England international in the summer.
Scott is contracted to Bournemouth until 2028, but the 23-year-old has opted against extension talks at this stage, but the club remain hopeful they can convince him to stay.
Bournemouth are pragmatic over their chances of keeping him, with Chelsea and Iraola's Liverpool closing in, and they could demand around £100M to sell the former Bristol City playmaker.
Club owner Bill Foley has offered an insight on the latest picture and he had a note of warning for Scott over making the right decision.
"We'd love Alex to stay here and sign a new contract and be part of this team for the long haul.
"We haven’t given up, but sometimes players get stars in their eyes, and think Chelsea or Man City is the right place to go.
"We believe, if we keep on buying infrastructure and a common thread of leadership across the team, then we'll start keeping more and more players.
"We have to prove to players this is a place they want to be, and want to stay, and not just move on - that's the way we really build a successful team."