The 22-year-old Bath man will have a scan on Saturday.
If Watson, who missed the autumn internationals with a broken jaw, is ruled out, then it could present an opportunity to Gloucester's Jonny May.
England, Grand Slam winners in 2016, start their title defence at Twickenham on 4 February.
England winger Anthony Watson is a doubt for the Six Nations opener against France after suffering a hamstring strain.