If the deal does go through, Parish will remain in charge of football-related decisions, but says Harris and Blitzer would be involved in major discussions over budget.
"There are very serious conversations going on and I will remain the single largest shareholder along with David and Josh," Parish told Sky Sports News HQ.
"The day-to-day decision making control will remain the same. They will bring some fresh ideas and some fresh input which will be great.
"But I think the guys recognize that having a UK partner retains the soul of the football club which is really important and it’s important to me that my three other partners will stay involved as well.
"It will be a much broader investment base and everyone is signing up to a commitment to improve the stadium. So it’s an exciting time and if it comes off I think we can make some major developments for the club."
Parish currently owns a 25 per cent stake in the club, the same percentage as co-chairman Stephen Browett and fellow owners Jeremy Hosking and Martin Long.
The quartet, also known as CPFC 2010, acquired Palace in 2010 and secured promotion to the Premier League in 2013, three years after the club had been placed into administration.
Browett, Hosking and Long will dilute their shareholding if the investment from Harris and Blitzer is secured, but will remain involved with Palace.