When the former Birmingham City owners took control of the Hammers in a £50 million deal in January, they rescued the club from the brink of financial meltdown.
The east London club now sit just three points above the relegation zone ahead of Saturday's Premier League encounter with in-form Arsenal.
Zola admits he meets Gold and Sullivan on a frequent basis at the club's training ground and on matchdays, but insists their influence has never compromised his role as manager.
Although Zola denies the duo ever giving him advice on players or tactics, he did admit they were very hands on.
"They like to know, they like me to explain what we are trying to do. I like that. They have been very good," Zola told Sporting Life.
"One of the owners comes to see the preparation [on match days]. I think that's normal. There's nothing wrong with that.
"I have no problem with that. It's not an issue. I like it when they come here and see what we are doing, so they can keep an eye on what we do."
West Ham face a critical period with encounters against fellow strugglers Wolverhampton Wanderers and Stoke City on the horizon, after Saturday's encounter with a Gunners side who will go top of the league if they win.
Tricky ties against Liverpool, Manchester City and Everton also loom for the Hammers in the end of season run-in, but Zola insists he's not worried about being sacked.
"I don't spend much time worrying about my future," added Zola.
"My future depends on what I can give. My focus is on making sure I give 100 per cent focus and then 'que sera, sera'.
"I can try hard and try to do a good job, and maybe the situation is not correct and things don't go very well.
"In that case, I cannot do anything. But it doesn't stop me working hard and being honest for the people I'm working for."
England fringe striker Carlton Cole is likely to return to West Ham’s starting line-up after being rested last week but Zola will be without Scott Parker who picked up a leg injury.
The Italian is hopeful of a similar performance to the one that secured West Ham a goalless draw at the Emirates last year.
"Obviously on paper, before the game Arsenal are flying now," said Zola.
"They are playing against a West Ham side that hasn't been playing very well and our away form is not the best but football is football and I always hope."Become a fan of Goal.com UK's Facebook fan page for all the latest news and insight into everything related to the beautiful game!