Ralf Schumacher faces a race against time to be fit for next week's French Grand Prix after a heavy crash landed him in hospital on Sunday.
Mario Theissen, motorsport director of Williams's engine partners BMW, said that there were doubts about the German driver's presence on the starting grid for the July 4 Magny-Cours race.
"There is clearly a question mark (about his participation)," said Theissen at the U.S Grand Prix.
"I cannot tell now what it will be but it has to be his own decision.
"He will stay here overnight in the hospital just as a precaution and tomorrow (Monday) he has to decide what to do."
Schumacher crashed on the fastest part of the circuit at Indianapolis, spinning on the banking at turn 13 where speeds reach around 320kph and slamming backwards into the wall before coming to a stop in the middle of the track.
Medical staff spent more than 10 minutes gingerly extricating Schumacher from the shattered car before taking him to hospital for precautionary checks after he had complained of back pains.
"He is in a lot of pain," said team head Frank Williams. "Everything works, his stomach is a bit upset, pretty bruised but he's basically sound.
"I think he'll probably be there for several days on my interpretation of what I've heard so far."
MONZA MISS
Last September Schumacher missed the Italian Grand Prix at Monza after a similarly high-speed crash in testing at the circuit left him struggling to overcome concussion.
Williams's former technical director Patrick Head, now elevated to head of engineering, recently suggested that Schumacher had been still suffering the after-effects of that crash well into the new season.
Theissen said it was too early to evaluate Schumacher's condition, although he had escaped serious injury.
"I went to see him in the medical centre, I talked to him," he added. "He said he could move all his bones, he reported a back pain so he was quite okay talking to me.
"I cannot really judge on the impact of such an accident.
"I think if the racing driver is ready to race, it is obvious that he will race. If not, we have to see what to do."
Williams have an official reserve driver in Spaniard Marc Gene, who is eager to be considered as a replacement for departing Colombian Juan Pablo Montoya and stood in for Schumacher last year.
Three-times world champion Niki Lauda meanwhile urged Schumacher, last year's winner in France, to get back behind the wheel as soon as possible.
"A driver of his calibre should be able to forget about something like this pretty quickly as long as he's not seriously hurt," said the Austrian.
"He's got to get back in the car and drive as soon as possible. As long as there's no pain he's got to start driving right away.
"He might have some muscle pain but that's something that can be taken care of fairly easily."
