The Spanish stopper managed to keep a clean sheet against Antonio Conte’s side at the weekend, as West Ham picked up an unexpected victory.
Moyes has now hinted that Adrian will retain his place for West Ham’s midweek match against Arsenal, but he does plan to recall Joe Hart in the future.
“Hart will play a lot of games this season, I’ve got no doubt about that,” Moyes said.
“[Adrian kept a] clean sheet, didn’t make any mistakes, so I’d have to say on that I would think so.”
Hart knows that he will have to break back into West Ham’s team, if he is to go to the World Cup with England.
Gareth Southgate has already suggested he won’t pick players who are not featuring for their club sides.
Adrian does have possession of the number one shirt at the moment though, and if David Moyes’ side continue to impress, Hart could face a tough task to break back into the team.
West Ham’s win over Chelsea has pushed Moyes’ side up into 18th place in the Premier League table, and eased some of the pressure which was building on Moyes at the London Stadium.