The former Fulham forward is yet to feature under new boss Harry Redknapp thanks to a hip injury that has kept him out since November's 1-0 defeat to Stoke City, but hopes to return early next year after undergoing a successful operation.
"I'd like to think I'll be back available in the next four or five weeks," he told the club's official website.
"I had an operation three weeks ago and am now working on getting fit. My fingers are crossed for a smooth recovery."
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The Hoops finally recorded their first win of the season at the 17th attempt against Fulham on Saturday, and Zamora is confident that his side can now go on to replicate last season's great escape from relegation.
"It's going to be tough, but when I came here in January it was an uphill struggle as people saw it and we overcame it then," he continued.
"We've got a better squad now than we did then so I see us doing exactly the same as we did last season - but hopefully we won't leave it to the last game this time!"