Carroll has endured a difficult spell at Anfield since making a then-British record £35 million transfer from Newcastle United in January 2011 and was loaned out to the Hammers late in the transfer window.
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The 23-year-old was highly impressive on his West Ham debut against Fulham despite suffering an injury in the second half.
Sam Allardyce's team won 3-0 on the day and Gold is determined that Carroll's experience at the club will be "the difference" in inspiring the good form he struggled to keep up with the Reds.
"The manager of WHU [West Ham United] wants AC [Andy Carroll] the players want him, the captain wants him, the fans want him, the owners want him," Gold posted on his Twitter account on Thursday. "That's the differance (sic)."
Carroll was ruled out of contention for a place in the England squad for the upcoming World Cup 2014 qualifiers due to the hamstring problem he suffered on Saturday, which will rule him out for six weeks.