According to NBC Sports' Drew Shiller, the parade was originally scheduled for Saturday at 3:10 p.m. ET, but the event's Facebook page revealed that it will not take place.
Jason McIntyre of The Big Lead reported in July that Thompson punched Green at the ESPYs after-party.
It was reportedly the result of Green attempting to apologize to Thompson for snubbing an attempted handshake at the conclusion of Golden State four-game sweep of the Cavs in the 2018 NBA Finals.
In response to the report, Green said it was inaccurate and then poked fun at the LeBron James-less Cavaliers, per Grant Liffmann of NBC Sports Bay Area:
Green also addressed the situation in an ESPN The Magazine interview with Sam Alipour on Thursday.
When asked about his feud with Thompson, Green said, "Was it ever a rivalry?"
He then added, "I want people to believe what they want to believe. If you were there, you know. No big deal."
With the parade canceled, the next big date on the schedule for the Cavaliers is Oct. 17, when they open their regular-season slate against the Toronto Raptors in Toronto.