Simmons - who rose to fame for his popular series of aerobic videos Sweatin' to the Oldies - died aged 76 at his home in Los Angeles on July 13. His cause of death is still pending an investigation.
Before his death, Simmons distanced himself from a forthcoming biopic about his life starring Shore.
Shore, however, recently told TMZ that the TV personality "wanted me" to make the biopic.
"I don't even know if that was him tweeting the whole time to be honest... I don't know who that was," he said.
Responding to Shore's comments, Simmons's staff shared on X/Twitter on Wednesday (July 31): "You've seen here on Richard's account what he had to say about the biopic.
"We'd also like to share the following statement from Richard's brother, Lenny. 'Dicky absolutely wrote his own posts. He worked on them a week in advance, going over and over them to get the right message. He would often read them to Cathy and I beforehand. What he has NOT done was to text, email or call Pauly with anything; not even to wish him 'Good Luck' as Pauly has stated many times.'"
The Independent has contacted Shore's representatives for comment.
Shore's short film The Court Jester premiered at Sundance Film Festival earlier this year and a feature-length version is currently in development at Warner Bros subsidiary The Wolper Organization from writer Jordan Allen-Dutton.
The Encino Man star said previously that he was "up all night crying" after Simmons criticized his project.
"Richard, how do you not approve of this movie? I mean, really, who's better to play you in a movie than ME? Leonardo DiCaprio's not gonna play you. Brad Pitt's not gonna play you. I'm perfect. Everyone already thinks I'm you. We're the same," he wrote on Instagram in April.
The statement came after Simmons tweeted: "I just read that a man that I don't know is writing my bio pic starring Pauly Shore. I do not approve this movie. I am in talks with major studios to create my own biopic with some help. Wait for this movie."
Shore previously told Variety that his movie was "all about love," regardless of Simmons's lack of blessing.
"It's never been vindictive. I'm not Borat. I'm not 'let's make fun of someone.' It's the opposite. At this point, it's an unauthorized biopic and they're made every day," Shore said. "Yes, I want him to put his pixie dust on this and say, 'Go for it, Pauly.' We don't want to bug him. We want him to be left alone and we don't want to bug him. We want to pay homage to him and kiss his feet and say he's done beautiful stuff."
