The Spanish goalkeeper returns to the starting XI with on-loan Joe Hart ineligible to face his parent club, and Moyes expects the No13 to be in for a busy afternoon against the champions.
However, Adrian excelled in the narrow 2-1 defeat in the reverse fixture at the Etihad before Christmas and the manager is backing him to produce the goods again at London Stadium.
“I hope he plays that well against Man City that he is available for the next one, that's the plan,” said the boss, when asked if Adrian has the opportunity to stake his claim for the final four games of the Premier League campaign, and to start next season as the first-choice stopper.
“If you get in and you do well, you're never going to play Man City without your goalkeeper having to play well, you've got to play well so we need a big game from Adrian on Sunday.”
You're never going to play Man City without your goalkeeper having to play well
Moyes was also asked if Hart would remain in east London, but refused to be drawn on the futures of either of his two senior goalkeepers.
“There are certainly no talks about whether it's Adrian or Joe Hart or anybody because until we are in a position of safety, we won't me making any decisions like that where we are going to be. So no, we've not discussed them.”
On the injury front, Moyes is expecting to have the same squad, bar Hart, available to face Pep Guardiola’s side to the one which drew at home with Stoke City and lost out late on at Arsenal.
Manuel Lanzini is pushing for a return to the starting XI, while young goalkeeper Nathan Trott is set to be promoted to the first-team squad.
While he may not be available to face City, midfielder Pedro Obiang is edging closer to a return from the knee injury he suffered in the Emirates FA Cup tie at Wigan Athletic in late January and could be fit for the final three games of the season against Leicester City, Manchester United and Everton.
“I think near enough everybody is back,” Moyes confirmed. “There is a chance that Pedro Obiang could be among us maybe for the last week of the season but at the moment, everybody who was available last weekend is available for Sunday.”
Aside from the ineligible Hart, Winston Reid (knee), James Collins (hamstring), Sam Byram (ankle) and Michail Antonio (hamstring) remain on the sidelines.