Midfielder Nolan suffered the injury in training last month and was told that he should be sidelined for no more than eight weeks.
And the former Newcastle United man has revealed that he is making good progress and hopes to be back in contention early next month.
Nolan told West Ham's official website: "The normal recovery time for an injury like this is six to eight weeks, I'm only two-and-a-half weeks into it at the moment.
"But I've only had positive feedback from the specialists so far. 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.
"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.
"Tuesday was the first time I've been able to get out and do a bit of work with my arm. It's feeling a bit weak at the moment, but in the next week or two I'll be building it up.
"Hopefully I'll be back to the fitness level I was at before."
Sam Allardyce's West Ham travel to Hull City in the Premier League on Monday.
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