The winger, who is enjoying his second spell with the Eagles having returned to the club from Manchester United in 2014, has made his stance public after another impressive season.
Will Wilfried Zaha sign a new contract?
However, the 28-year-old remains on Palace’s books and is firmly in Patrick Vieira’s plans following his appointment as manager earlier this month.
Palace chairman Steve Parish has confirmed Zaha will only be allowed to leave the club if an offer meets their expectations, but Woosnam believes there is a chance the Ivory Coast international will finish his career at Selhurst Park.
Speaking to TIF, he said: “My feeling is the most likely outcome is that he will sign a new contract with Palace at some point and finish his career there.
“I imagine a lot will depend on how he gets on with Vieira and how Palace do this season. If they’re looking better in terms of being a more progressive outfit and he can see something building, then perhaps he’ll be inclined to stay.”