It is currently unclear whether Zaha is part of new United boss Louis van Gaal's plans, but Parish has revealed that he would be open to discussions.
"It depends on what the new Man United manager wants but also what my manager wants," he is quoted as saying by the Croydon Advertiser.
"My manager has got to be convinced that it would be the right move for the player and the club.
"Tony has certainly shown enthusiasm during the season for that and knows what a fabulous player he is. But the circumstances for the player and the money and for everything would have to be right."
As it stands, Zaha will return to pre-season training with United next month.