Parker is set to leave Fulham and has been in talks with the club over the mutual termination of his contract before entering into negotiations with the Cherries.
Jonathan Woodgate, who took over at Bournemouth following the sacking of Jason Tindall last season, is under contract until July 1, although the players will return for pre-season testing on Saturday and begin training on Monday.
Parker is less than a year into a three-year deal — signed in September 2020 — but is expected to leave, following friction between him and the club’s owner, Shahid Khan, and his son and director of football at Craven Cottage, Tony Khan.
Former England midfielder Parker was unable to prevent Fulham’s immediate return to the Championship last season, with their relegation confirmed with three games of the season remaining.
The Championship season gets underway on the weekend of August 7, with the fixtures to be announced tomorrow.