Nolan had been expected to miss around eight weeks of football, but the 32-year-old now hopes to be training with his teammates sooner.
"I'm sort of hoping in my own head that it won't be eight weeks, I'd rather it be only six. Anything before that would be another bonus," he told the club's official website.
"I'm just taking it day by day now because I'm seeing different people at different times. As it goes along I'll find out more about what I can do with it. In the end it'll come down to how much pain threshold I can take really."
West Ham continue their Premier League campaign on Monday when they face Hull City at the KC Stadium.