Jacobsen, 31, was a first-team regular at Upton Park following his move from Blackburn last summer but now seems set to make a return to his homeland, and FC Copenhagen are hoping to win the race for his signature.
"I am considering returning home to Denmark. That is a possibility," he said.
"That is not to say that this will happen. I keep all doors open.
"[A return to Copenhagen] could be really fun and it could really tempt you. It feels like it is at the top level."