With Calum McFarlane in interim charge for the rest of the season following the sacking of Liam Rosenior, Chelsea look in dire straits as they aim to qualify for the Champions League.
Palmer could see his future influenced by whether the club secure Champions League qualification for next season, as anything less could trigger him to force a move away from West London.
The England star has already been linked with a move to Manchester United and Barry, speaking to Midnite, believes that he may look elsewhere if the club becomes more unstable.
“Any player wants to be playing in a settled dressing room at a settled club,” he said. “If you’re in a dressing room that is perhaps slightly toxic, it is hard to go into training and perform every day, it’s not nice.
“We all know the dressing room is so strong if you get two or three players starting to doubt the manager’s beliefs or his methods, it naturally creeps in. If those few players aren’t happy, they’re not going to be performing at the levels they can if something’s eating away at them, and it can leak into the whole team’s performance.
“If that was the case at Chelsea it would be affecting the dressing room.
“Any player, Cole Palmer and others, if they aren’t seeing a long-term settled future at Chelsea, it’s natural for them and their agents to start looking and thinking ‘where can we go and achieve things’ in what ultimately is a quick career as a football player.”
Palmer is tied to terms through to 2033 and as he looks towards the World Cup this summer, he may be thinking about what direction Chelsea are heading in ahead of next season.