Widespread reports on Tuesday morning suggested the England striker was a target for the promoted club, with an initial loan deal and a future fee of £15 million being mooted for a player who cost Liverpool £35m just 18 months ago.
Liverpool manager Brendan Rodgers has already said that he may consider allowing Carroll to leave Anfield on loan as the club close in on Roma striker Fabio Borini.
While Gold is adamant that West Ham are yet to contact Liverpool regarding the striker, he has hinted the London club would be interested in a deal.
"I am not aware of any talks between ourselves or Liverpool over Andy Carroll," Gold told the BBC.
"But that's not to say we don't have an interest should he become available."
Carroll has scored six league goals for Liverpool in 42 appearances since his move from Newcastle in January 2011.