Croydon council will consider the planning application for a new main stand, which will increase the ground’s capacity from 26,000 to 34,000, on April 19.
Parish said last month Palace were exploring selling the naming rights to Selhurst Park and has now confirmed they are open to a deal to change the name of the ground.
The chairman told Standard Sport: “If it was the right number and something that helped us build it [the new main stand] better or faster then it is something we would look at it.
“Selhurst Park is a nice name... probably I would not personally mind as much because my goal is improving the club. My primary focus is to make the club better. But all of these things have to be weighed up. We are not going to give them up easily. I think people would understand if it is the right answer for the club and if it is a good association as well. That matters.
“It might make the difference between doing it exactly how we want and making some compromises. It is not a decision that we would definitely do it. We would look at all options.”
Palace will also consider a deal that would keep the name Selhurst Park but that would be less lucrative.
Should Palace get planning permission next month, the club hope work will start at the end of next season and they hope the redevelopment will be completed for the 2020-21 campaign. However, if councillors reject the scheme next month Palace fear any new plans would not be approved in time for the stand to open in August 2020.
Parish is urging fans to support the application on the council’s website and said: “It would be huge for the club and the area. We are working with the council and the stakeholders on any issues. But there don’t seem that many. The vast majority feel it will be a good thing.”