Moyes is edging closer to the end of his current deal but has suffered a series of poor recent results.
West Ham are winless in all competitions this year, with their latest Premier League defeat coming against 16th-placed Nottingham Forest.
The Europa Conference League holders are ninth after picking 36 points from 25 matches and next host Brentford on Monday.
The former Manchester United and Everton coach, whose contract expires at the end of the current season, was criticised by West Ham fans after their 6-0 loss to Arsenal earlier in February. It was West Ham's joint-heaviest home defeat in the league.
Moyes returned for a second spell at the London Stadium in 2019, replacing Chilean Manuel Pellegrini.
"There's a contract there for me, I'm the one deciding I want to wait until the end of the season, to make sure everything is correct, and concentrate on this season," Moyes told reporters on Friday.
"I've really enjoyed my four years. I'll see my contract out."
Moyes said his focus lies on their next match against Brentford, who are 14th in the league. He said Brazilian midfielder Lucas Paqueta is in contention to start on Monday following an injury.
"Paqueta's back in training, he's very close to returning and hopefully that will give us a huge boost," Moyes said.
