The 33-year-old moved to the United States in March after being allowed to leave Manchester United and scored on his MLS debut in a 2-2 draw with Montreal Impact.
Although Schweinsteiger does have the option of a year-long extension with the club, the Germany World Cup winner is eager to keep his options open.
The Bayern Munich legend told Eurosport: "I signed for only one year because I wanted to see how everything goes.
"The state of things is that I have this contract but I don't have anything else yet and I'm open to everything. Then we'll see what happens."
Schweinsteiger has made 24 appearances for Fire thus far, scoring three goals and registering two assists.