The 38-year-old's contract with the MLS club expires on December 31 and reports have circulated that he could return to one of his former clubs, with both Inter and Manchester United linked speculatively with his signature.
When asked whether Sunday's MLS play-off against Minnesota United would be his last game for Galaxy, he replied: "Could be.
"There are no other thoughts, I respect my contract. If I leave you will have less to write about.
"If I stay you will still have something to write about. Let's see what happens. But let's focus on the playoff. I think [my future] is not the right thing to discuss.
"I've had a good time, good experience. I've learned a lot on how it works here, still a work in progress.
"I've enjoyed it and that's the most important. I came back from my injury and came like a little kid that just wanted to enjoy football. MLS gave me the opportunity and I took it."