Gold says the club are keen to retain the services of the 58-year-old former Bolton, Newcastle and Blackburn boss, whose current deal expires in the summer.
"What we promised and, what Sam promised us, is that at the end of the season we would sit down and discuss Sam's position," Gold told talkSPORT.
"I'm very optimistic that Sam will be our manager next season. But we have to sit down.
"The agreement with the board was that we would sit down at the end of the season, not when we're safe - we are not mathematically safe as we speak."
Asked if he was worried Allardyce could agree a move elsewhere before then, he added: "There's always the danger that a bigger club comes in. There is that danger.
"Having said that Sam has given his word that he will sit down and discuss his contract at the end of the season and I trust him."
Allardyce was appointed Hammers boss in June 2011 and led them back into the Premier League in his first season in charge, despite some criticism from fans over the team's style of play.
The club are currently 12th in the top-flight table having amassed 33 points from 28 games.