Carroll is on the sidelines at the moment with a hamstring injury he suffered earlier this month.
The England international striker has been ruled out of all action for six weeks, according to BBC Sport.
Gold has predicted on Twitter that the 27-year-old will prove his doubters wrong when he eventually regains his fitness.
Andy Carroll will be back in 3 or 4 weeks to prove many people wrong. dg https://t.co/Z0eFeWyGtH— David Gold (@davidgold) January 16, 201
Carroll has struggled with injuries for the past few seasons and has yet to show what he is capable of at West Ham.
The former Newcastle United and Liverpool striker has scored three goals and created five chances in 13 Premier League appearances so far this campaign.
The Englishman has a pass accuracy of 63% and a shot accuracy of 61%, and has won 43 headers, three dribbles and one tackle.
West Ham are fifth in the Premier League table at the moment with 35 points from 22 matches, four points behind Tottenham Hotspur, who are currently fourth and occupy the final Champions League spot.