Palace are virtually guaranteed Premier League football after their win over Manchester City on Easter Monday - their third win in four games.
The club were linked with a takeover by American billionaire Josh Harris late last year.
Parish says they only need investment in order to improve Selhurst Park.
"The only reason for us to get money in is to improve the infrastructure. There is no rush and we are in a good place. If it happens, it happens," he said.
Parish, who was speaking to BBC London 94.9, added: "We've done well enough that I think we can fund the player things we need to do out of our own resources.
"We are long overdue some ground improvements. They are very costly.
"We need to make sure we get that done. If that means bringing in other people, and they are the right people, then we'll do it."
Parish has been co-owner and co-chairman of Palace since leading the CPFC 2010 consortium deal to save the club from extinction in 2010.
The Eagles won promotion to the top flight in 2013 via the Championship play-offs and recently announced a pre-tax profit of £23m for the financial year to June 2014.
Harris is the principal owner of two sports teams in the United States - National Hockey League side New Jersey Devils and the Philadelphia 76ers of the National Basketball Association - and recent newspaper reports have suggested he is close to buying Palace.
However, Parish may remain at Selhurst Park even if the south London club are sold.
Selhurst Park Crystal Palace have played at the Archibald Leitch-designed Selhurst Park since 1924, and Parish wants to make "some major improvements" to the ground
"It depends what the situation is - something else could happen tomorrow," said Parish.
"Right now, the people we've spoken to want me to carry on being involved. If that's the right thing for the club then I will be.
"If a Roman Abramovich-type or Abu Dhabi person wanted to buy the club and was prepared to put that kind of money [in], then obviously it is a different conversation."
Parish is adamant that improvements to Selhurst Park, Palace's home since 1924, are his priority.
"I want to leave a legacy. A few years in the Premier League isn't my idea of a legacy," he said.
"I won't be happy until we've made some major improvements to the ground and are a solid Premier League team. There's lots of work to do.
"We need to put more seats in and make us a better attended club as that gets you to another level.
"If we can get over the line in the league we can start making some really positive, bullish plans for the club."