The 23-year-old delivered an impressive performance on his first senior England start in the 7-0 Nations League thrashing of Croatia on Saturday and earned strong praise from head coach Thomas Tuchel.
Chelsea had more than one offer, understood to be worth in excess of £60 million, turned down by Bournemouth during the last transfer window. The west London club remain highly interested and view midfield as a priority area following the sale of Enzo Fernández to Manchester City.
Although Bournemouth have insisted Scott will not be sold in January, Chelsea are prepared to wait until the summer if necessary. Scott will enter the final year of his contract at the end of the current season.
Liverpool, managed by Scott’s former Bournemouth head coach Andoni Iraola, and Arsenal are also monitoring the player. Tottenham Hotspur, Manchester United and Manchester City have already strengthened their midfield options in recent windows.
Bournemouth have attempted to persuade Scott to sign a new deal, but talks have stalled and both parties have agreed to concentrate on the season ahead. Scott is expected to win his third England cap when the side face Czechia at Wembley on Tuesday.
Chelsea’s interest forms part of a wider search for midfield reinforcements, with the club also having come close to signing Monaco’s Lamine Camara on deadline day.