The South Korean star, a fan favorite during his time at Old Trafford, says he doesn't think supporters mean to offend but is aware the song makes younger players feel uncomfortable.
Park played more than 200 matches during his seven seasons at United, winning multiple trophies including four Premier League titles and one Champions League trophy.
Despite leaving in 2012, fans still sing his song and they did so again in a game this season against Wolverhampton Wanderers, who had just signed South Korea international Hee-Chan Hwang.
"In Korea, things have changed a lot," Park told the club's official UTD podcast.
"It is true that historically people have eaten dog meat but these days, particularly the younger generation, they really hate it.
"I know that United fans don't mean any offence to him for that song but still I have to educate the fans to stop this word [dog meat], which is these days usually a racial insult to the Korean people."
'I just accepted it as a player'
Park, who joined United from Dutch side PSV Eindhoven in 2005, says he felt uncomfortable when he first heard his chant as a player but initially considered it a cultural change that he'd have to get used to.
Now retired from football, he is conscious that times have changed and he's urged fans to stop singing it.
"It was one of the things I had to accept because I never thought fans would create a song with bad meanings," he added.
"They always make a song to cheer up, to give energy to the players, be proud of the players, that's my thought. That's why I just accepted it as a player."
On its website Manchester United said it "fully supports Ji-sung's comments and urges fans to respect his wishes."
Last month South Korea's President Moon Jae-in said there might be a need to prohibit dog meat consumption amid debate over the controversial practice and growing awareness of animal rights.