Xherdan Shaqiri may be left behind in Liverpool on Monday when the Reds travel to Serbia to take on Red Star Belgrade in the Champions League.
Group C leaders Liverpool face Red Star on Tuesday night, but Klopp fears Shaqiri could be targeted by Serbian fans.
Shaqiri was born in Kosova and has made a point of celebrating his heritage playing for Switzeraland, something Serbian nationals object to.
Serbia do not recognize Kosova as an independent country, and Shaqiris actions have drawn a hostile reaction from Red Star fans.
Red Star supporters were banned from Anfield in the reverse fixture last month, but Shaqiri was still booed by rogue fans inside the stadium whenever he touched the ball.
The Telegraph claim Klopp is leaning towards dropping Shaqiri from the squad to avoid the game becoming a political spectacle.
Klopp does not want to risk the tensions distracting his Liverpool players, as his side look to put some distance between them and Napoli in Group C.
Liverpool are not concerned about Shaqiris safety, but Klopp is worried the forwards inclusion could create a circus.
I just go there to play a football game, Shaqiri said over the weekend.
It is not about politics it is about football. I worry about nothing and go to play. I had this already at the World Cup so I know I can handle this no problem.
Shaqiri will be disappointed if he is left behind in Liverpool, having made an impressive start to his career with the Merseysiders.
The Switzerland international has yet to break into Liverpools starting eleven, but has been excellent every time he has been called upon.
The game against Red Star would have been a perfect opportunity for Shaqiri to start and impress again.