Mamadou Sakho was crucial to helping Crystal Palace avoid relegation this year
Sakho spent the second half of the season on loan at Crystal Palace and played a key part in helping Sam Allardyce's side avoid Premier League relegation.
Parish last month confirmed Palace's interest in signing him this summer, but now the chairman admits they could be priced out by Liverpool.
Sakho was frozen out at Anfield during the first half of the campaign after falling out with manager Jurgen Klopp, but the club appear to be reluctant to let him leave on the cheap.
The Evening Standard claim Liverpool want £30million for the France international, who cost the Reds £18m from Paris Saint-Germain four years ago.
Steve Parish plays down Mamadou Sakho move
Crystal Palace play down move for Liverpool defender Mamadou Sakho
“I think that is going to be a very difficult one for us to do,” Parish told the Evening Standard when asked about a permanent move for Sakho.
"I think Liverpool want a big number for him. That is a tough one to make happen on a permanent basis. We need to look at the budgets and be realistic.”
Parish admits Palace are looking for a long-term manager after the departure of Allardyce earlier this month.
Mamadou Sakho fell out with Jurgen Klopp last summer Liverpool fans rage as Mamadou Sakho celebrates with Christian Benteke Sun, April 23, 2017
Mamadou Sakho has sent Liverpool fans mental on Twitter after celebrating Christian Benteke's goal for Crystal Palace
Play slideshow REUTERS 1 of 9
Get Quotes on Home Insurance
Liverpool fans are furious with Mamadou Sakho after this celebration
The last manager to spend more than two years at Selhurst Park was Neil Warnock and Palace have bounced between stop-gap solutions since his first spell ended in 2010.
"We really want somebody who feels they can come in and help us improve the footballing side of the club over a long period of time," Parish said.
"That is what we are looking for. In the past we have had managers like Steve Coppell who have been at the club a long time and helped build the club.
"If we could get one of those relationships again that would be preferable."