Warnock held talks with Zaha on Wednesday night in an effort to convince him to return to the club at which he spent 11 years making his name.
Warnock will hold his first training session on Thursday morning and his first press conference at 5pm, and is eager to add to his squad before the transfer window closes on September 1.
Zaha has failed to impress new Manchester United manager Louis Van Gaal and was an unused substitute in the embarrassing 4-0 Capital One Cup defeat by MK Dons on Tuesday night.
The winger has failed to start a Premier League match at United since joining the club in a £15m move to Old Trafford in 2013, and was sent on loan to Cardiff City last season.
Warnock told Sky Sports News HQ: “I think Wilfried needs us like we need Wilfried. He’s been at a big club like Man United, and it is a big club, and he’s probably got a bit lost in the chambers there.
“He could have gone to three or four clubs and I spoke to him last night for a good hour and I think people think wrong of him at times with what people say about his attitude.
“Wilfried has always had a great attitude for me. He wants to learn he wants to do extra training so we are going to let him do that."
Palace have lost their opening two fixtures of the Premier League season and chairman Steve Parish has promised fans that Warnock will be given the money to strengthen his squad.
"There's plenty more work to do," Parish told Sky Sports News HQ.
"We've got the transfer window closing on Monday and I think he'd want to bring a few in, so hopefully we've got some more good news for supporters in the next few days."