Wenger has faced mounting pressure this season, with his Arsenal side losing their fourth successive away match in the league on Monday to relegation battlers Crystal Palace.
The 3-0 defeat at Selhurst Park has left sixth-placed Arsenal sitting seven points adrift of fourth-placed Manchester City, although they do have a game in hand over Pep Guardiola's side and two over third-placed Liverpool.
And despite renewed calls from some Arsenal fans for Wenger to step down as manager when his current contract at the Emirates Stadium expires at the end of the season, Gold believes the Frenchman isn't under any serious pressure to vacate his role just yet.
The West Ham co-chairman has had to deal with Slaven Bilic coming under intense pressure due to the club's inconsistent set of results this season, although the club publicly backed their manager recently.
And Gold believes that Wenger is in a similar position and will end up staying on as Arsenal manager because he knows the club inside out.
"I don't really think Arsene Wenger is under serious pressure for his job," Gold told Goal. "The man has been there 20 years and everybody knows how he works and I think if he wants to stay that will be that.
"He will stay. The Arsenal fans are a bit like Manchester United's - they believe they have a right to trophies. They expect to win everything so this is very difficult for them.
"I think Arsene Wenger will be OK. He will weather the storm and I don't accept there is some sort of dressing room revolt going on.
"He has been there long enough to know how to sort that out."