The 23-year-old German played 38 times in his first season in English football but he now faces a tough decision on whether to return to his homeland to be closer to his family.
Pirates boss John Ward hopes to retain Broghammer and says he will talk to the player's agent in the coming days.
"Fabian is an intelligent boy with a lot of common sense," Ward told the Bristol Evening Post.
"He made the big decision to move away from his home in Germany at a relatively young age of 23 last summer and I have a lot of respect for him as a person for doing that.
"I'll have a meeting with his agent, who is in England at the moment, and we will see what happens after that."