Buck is anticipated to remain at Stamford Bridge after working for former owner Roman Abramovich, who was sanctioned by the UK government.
The West London club is racing against the clock to finalize the proposed purchase led by Boehly’s group by the June 8 deadline.
Although Boehly intends to make a lot of changes at the top, it is thought that Jonathan Goldstein, who was maybe considered as a replacement for Buck, will not be joining the board.
Goldstein’s ties to Tottenham Hotspur are said to have prevented the club from hiring him.
Marina Granovskaia, Chelsea’s director and top transfer negotiator, is also set to stay.
Buck and Granovskaia both played key roles in picking the preferred bidder alongside the Raine Group, the US bank selected by Abramovich to arrange the club’s sale.