Gold, who owns 62 per cent of the club with long-standing business partner David Sullivan, said Hansen still owed him an apology over "insulting" remarks the Scot made on Match of the Day in 2010.
"I think he said, a good chair is a chairman that doesn't sign autographs or interacts with fans," Gold wrote on Twitter yesterday.
"He also implied that a good chairman shouldn't have a football opinion. Alan Hansen is a pompous fool and owes me an apology."
Gold said the BBC had sent him footage of the programme, which he appeared in, but not Hansen's remarks.
He added: "It's interesting that after my feature on MOD [Match of the Day] the BBC sent my a copy of the show but cut out the insulting comments by AH [Hansen]."
The Hammers picked up their first away points since their promotion in a 0-0 draw with Norwich at Carrow Road on Saturday. Manager Sam Allardyce said: "That's three clean sheets from four since our return to the Premier League and that is a basis to build from."