Zaha was sold to Manchester United for £15million in January 2013 but has failed to shine and his Old Trafford future is shrouded in doubt.
Parish insists the 21-year-old winger would be welcome back in south-east London, but stresses the decision is up to Palace boss Tony Pulis - and United.
"Manchester United are not quite sure what they're doing with him so out of respect for them, it's not for me to talk about that," Parish told Sky Sports News.
"I'm sure that if he can, he'll try to be a permanent fixture at Manchester United this season.
"It's up to the manager, the players we sign
It's not up to me
I'm there to help him get the squad he wants.
"There's a sentimental value and I loved Wilf as a kid and he did sensational things for us.
"I know the fans would like him back and that will play a part, but in the end the manager will decide what we do."
Parish hopes to complete the signing of two players before Saturday's Barclays Premier League opener against Arsenal at the Emirates Stadium.
"We're looking at a Premier League midfielder
It's someone we're interested in and if we can get the deal right we'll try to do it," Parish said.
"Hopefully the other player will be here in the next couple of days and that shouldn't be the end of it, although it will be as much as we can do before the Arsenal game."
Parish revealed that the row over bonuses - the squad have demanded a bigger sum this season - has been brought to a successful resolution.
Source : PA
Source: PA