The 24-year-old suffered a fresh injury blow to his Achilles before the start of the 2013-14 campaign, with some reports claiming that the striker could be out of action for the rest of the season.
"We have spoken to specialists in America and Europe and have a complete understanding of what we are dealing with," Gold told SportsDirect News. "There is much that can be done to solve the problem. Andy is doing well in his recovery programme. I am hopeful he will be back in action within weeks, not months."
Without Carroll, who signed a permanent six-year deal with the club in the summer, the Hammers have not won a game since their opening-day victory over Cardiff City.