Sale Sharks' England fly-half George Ford is a doubt for the autumn internationals after suffering a torn thigh muscle in the defeat at Saracens.
The 31-year-old had to go off in the early stages of Saturday's 45-26 loss after attempting a long-range penalty.
England play the first of their four autumn Tests on 2 November when they face New Zealand.
"We don't know the length of time that will take to rehab at this point. We haven't got anything definite or concrete to tell you now," director of rugby Alex Sanderson said.
"He's important to us, King and country. Nationally important, he is.
"I can perceive [him] being back [after] not an overly long layoff given how he walked off the field but that's the only subjective analysis I've got on it."
Ford, who has won 91 caps for his country, is out of contract at the end of the season.
Sanderson added that they had held "positive talks" with him about extending his deal through to the 2027 World Cup.