Moyes took over from Slaven Bilic in November on an initial six-month contract, and he has since taken the Hammers from 18th in the table up to 12th, with four points now separating them from the relegation zone.
Reports earlier this month suggested that Moyes would leave the London Stadium this summer regardless of whether he kept the club in the division, although the former Manchester United boss has insisted that is not the case.
"No, that's definitely not the case. The situation when I came in was that I said I wouldn't make any decision until the end of the season, and I didn't want West Ham to make a decision either," he told talkSPORT.
"I said, 'let's see how it goes', because first and foremost we have to make sure we're a Premier League club. I was happy doing that, I came in on a short-term contract, I had no problem with that and that's the way I want it to remain. Anything what has been said is completely wrong – we'll decide at the end of the season.
"The job I want to do is to make sure West Ham are a Premier League club, and I want to see what West Ham can do in the future. This club has big expectations, they are pulling in nearly 60,000 people every game and I think it can get bigger and better."
The West Ham board also released a statement "categorically refuting" the report.