The former Eagles striker says the club have every right to hold out for the best deal they can for the Ivorian forward and has backed their £80million price tag.
Zaha has been strongly linked with a move across London to Arsenal this summer after reportedly telling Palace officials he wants to take the next step of his career and move to the Emirates Stadium.
However, that deal is going nowhere fast as none of the Gunners’ multiple bids have come anywhere close to meeting the players’ full valuation.
Arsenal’s hopes were dealt a further blow on Monday with reports German champions Bayern have now entered the race to sign Zaha.
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But Morrison believes, or perhaps more accurately hopes, the star will stay this summer – as chairman Steve Parish is under absolutely no pressure to sell.
“Every Palace fan will be happy if Wilfried Zaha stays,” the striker, who scored more than 100 goals for the Eagles, told talkSPORT host Jim White on Monday.
“I think he’ll come back and be the same model professional he is and churn out performances.