Harris has a net worth thought to be over $2 billion and already owns sports franchises in the United States - the NHL's New Jersey Devils and the Philadelphia 76ers in the NBA.
Parish and three other wealthy Palace fans - known collectively as CPFC 2010 - purchased the London club over four years ago as it sat at risk of administration and have overseen promotion to the Premier League under Ian Holloway before last term's impressive top-flight survival in the hands of Tony Pulis.
Though Parish concedes the consortium currently at the Selhurst Park helm are open to handing the club over to interested parties, he has played down recent claims in the British media that a takeover is on the brink of completion.
He told the Croydon Guardian: "There are always people who want to buy football clubs.
"Sometimes people approach you and it gets out, sometimes people approach you and it doesn't, but there is no imminent takeover.
"We are talking to a number of people on a number of fronts.
"I've always said that if somebody wanted to invest in the club and move it forward quicker than I or we can then we would entertain it.
"We look at all possibilities that are out there - and there are many - but people have been quite ahead of themselves on this one."
