Hart is unable to play due to stipulations of the loan agreement and Adrian coming in to take his place.
"There's certainly no talk on whether it will be Adrian or Joe Hart [as future no 1] until we're in a position of safety, or wherever we're going to be," Moyes explained.
"So no we've not discussed anything, to be honest."
Moyes is hoping for a performance good enough to keep Adrian in the starting XI for the remaining weeks of the campaign.
"I hope he plays that well against Manchester City that he's available to play the next one, that's the plan. If you get in and you do well [you stay in].
"You can't play a Manchester United or City and do well without your keeper playing well so we need a big game from Adrian on Sunday."