The 31-year-old has not played since aggravating a hip problem during the 1-0 defeat at Stoke last month, which resulted in surgery.
Zamora was originally expected to be out until the end of February but could now return a month early.
"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."
In his absence, QPR have parted company with Mark Hughes and last Saturday got their first Premier League win of the season against Zamora's old team Fulham.
"That win has given everyone a massive boost," the striker added.
"It's been coming a long time because we've been so close on so many occasions.
"Now we're looking to build on the good results and continue to climb the table."