Adarabioyo and Palmer, 23, have become close friends both on and off the pitch. Losing Adarabioyo would likely be a significant blow to Palmer, who values his friend's support and camaraderie.
It's understood that Adarabioyo, who also came through the Manchester City academy, was very supportive of Palmer during a difficult period in front of goal last season.
Despite being linked with a move, Adarabioyo still has three years left on his contract at Stamford Bridge, and there are no indications that he is seeking to leave the club.