The French driver's car hit a loose drain cover and was pitched into the barriers.
While Grosjean escaped unscathed, the U.S.-owned team estimated repairs to the car had cost them some $650,000. That assessment could change, depending on what parts can be salvaged and reused.
Steiner told reporters at the Japanese Grand Prix that he had spoken to Razlan Razali, chief executive of the Sepang International Circuit, about it but did not sound overly optimistic.
"Nobody agrees to you to give you this amount of money, you know. Nobody volunteers even if you are the best guy in the world, to give you this amount of money," said Steiner.
"I just spoke with them and made them aware that we don’t feel responsible for it. But I have not got any discussions or I haven’t got any 'no', I haven’t got any 'yes'," he said.
Sunday's race marked Malaysia's farewell to Formula One, with the grand prix dropping off the calendar from 2018.
Steiner said he had spoken to the sport’s governing body, the International Automobile Federation (FIA), whose race director Charlie Whiting is one of the key people responsible for circuit safety.
Whiting, who drove to the scene of the accident in the safety car, told drivers in their regular briefing, which was shared on social media, that the welds holding the drain down had failed.
The FIA then had all drain covers around the track re-welded as a precaution.
When asked if he would keep pushing for compensation until he got it, Steiner said: "You have to because I don’t feel we are responsible for this damage. What can we do?
"The good thing is that nobody was hurt. That is the most important thing. And then the damage we can sort out afterwards."
Grosjean finished Sunday’s race 13th and a lap down on Red Bull's winner Max Verstappen.
($1 = 0.7621 pounds)
(Editing by Alan Baldwin and Toby Davis)
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