The 58-year-old's current deal expires in the summer, but Gold has insisted that the Hammers are keen to extend his contract.
"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."
Allardyce took charge of West Ham in June 2011.