The Mexican has so far failed the score any points this year, leaving a question mark hanging over his future.
"Frankly, it is clear that we expected more when we made the agreement with him," Steiner is quoted by the Finnish newspaper Turun Sanomat in Austin.
"While it is true that he has had a lot of bad luck, particularly early in the season, when Grosjean collected most of the points and he (Gutierrez) suffered from technical problems that were not his fault.
"However, we have also seen quite a few opportunities to grab points in the second half of the season. So we will give him a few more races to show what he can do," he added.
Turun Sanomat also linked Kevin Magnussen and Felipe Nasr with Gutierrez's Haas seat, while it also said that "Sauber is not interested in taking him back".
Bahrain International Circuit - Winter testing