"As Rafa has already explained to the media, he and I have discussed the Premier League's proposal for a 39th game and we both have concerns such a move could damage the integrity of the competition. I expressed these thoughts at the time and still hold them today," said Parry.
"There's already an ongoing debate about a potential winter break and we are constantly talking about the demands being made on players these days.
"You have to look forward, but the popularity of the Premier League is based around the country's top teams playing in England.
"I don't have an issue with the idea being taken forward for further discussion but it's vital that the Premier League listen to key people both here and abroad and the reaction so far has been a negative one in many ways.
"We should consider any new proposal on its merits, but this has never been on Liverpool's club agenda. Our goal remains to build a bigger stadium in Liverpool to enable more of our supporters to watch us play there."