Bendtner arrived in South London for talks over a last-ditch move to Selhurst Park this afternoon, with personal terms and a medical agreed for the Danish forward.
Parish has revealed that the deal will go right to the wire and is dependent on Arsenal finding a striker to replace Bendtner before the 11pm transfer deadline.
He told Sky Sports News: "We're waiting to hear, I think it all depends if Arsenal get somebody else in.
"We don't know anymore than we did a few hours ago. We have contingency plans in place.
"I'm not confident, but I'm hopeful."
The Gunners are thought to be chasing a deadline-day deal for Chelsea forward Demba Ba, with an enquiry lodged over a season-long loan switch.