The former Bayern Munich and Manchester United midfielder joined the MLS club in March and scored on his debut in a 2-2 draw with Montreal Impact.
The club officially clinched their place in the MLS Cup play-offs with a 4-1 win over San Jose Earthquakes last month, giving Schweinsteiger a shot at silverware in his first season in the United States.
The 33-year-old's contract expires at the end of 2017 but reportedly contains an option for a year-long extension.
However, the ex-Germany captain is keeping his options open.
"I signed for only one year because I wanted to see how everything goes," he told Eurosport.
"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."