The two teams will meet at Selhurst Park on Sunday, with Leicester third and Roy Hodgson's side sixth and notably ahead of Manchester United and Tottenham.
During the summer, the Red Devils raided the Foxes and Eagles, but had to pay £130million overall for Harry Maguire and Aaron Wan-Bissaka.
Palace chairman Parish managed to hold firm when it came to Wilfried Zaha and he believes clubs outside the traditional big six are no longer reliant on selling to survive.
"It is clear what has changed in the Premier League is the Leicesters and Crystal Palaces don't have to sell to survive, and if we think we can do more with the money we will, but we take everything on its merits," he said.
"If there is a signal that has been sent out this summer it is we will sell if it's the right money, and if it's not we won't sell."
Wan-Bissaka and Zaha highlight this, with the former departing Selhurst Park for £50m despite making only 49 appearances for the first team.
Meanwhile, fellow academy graduate Zaha failed to earn a move, but the form of the winger has improved and he helped Hodgson's team fight back to draw 2-2 at Arsenal last weekend.
VAR was prominent throughout and disallowed a potential late winner for the Gunners.
Parish added: "What is interesting, and I have been doing this for 10 years, is it's the first time I have come away from stadiums having played away where the big home teams are moaning about decisions.
"The guy in the (VAR) box is making decisions based on what he sees. I think in spite of everyone's best intentions there are other influences when it is just left to the referee."
The Palace chairman was speaking after revealing plans for the club to obtain Category One academy status by the start of next season.
Several factors are behind the decision, and one was to make sure they avoid missing out on people like James Maddison, who is now a key man for the Foxes.
A part of why the club, then-managed by Alan Pardew, did not go ahead with signing Maddison was because they felt he was not ready and were unsure if putting him in the development squad would allow him to progress.
Had Palace been Category One status, the playmaker, then at Coventry, may have made the move.
Parish added: "On Sunday we play Leicester, who have fantastic, exciting 22 and 23-year-olds.
"Five or six years ago people would say 'you can't play with that many kids in the Premier League', so it's fantastic.
"How grown up and mature these guys are is impressive, and it is the other care around the boys that the Premier League and Cat One has implemented which has really gone a long way to making people more ready."