Now in an attempt to clear up some of the rumours, Simmons's brother Lenny has told Entertainment Tonight the star "needs some time for himself" and asked people to respect his brother's privacy.
"I talked to him on Sunday, he was doing great. He was asking about our renovations to our home. And we had just gone to see the Broadway musical, Beautiful," Lenny said.
"We talk every Sunday. He calls me and we have a great conversation and then he talks to my wife. He probably talks to my wife longer than he talks to me.
"After all those years, I don't know how he did it. He was on 24/7, at least. ... People were always calling him and he was always good enough to want to talk to them," he said.
Lenny also dismissed suggestions that housekeeper Teresa Reveles has anything but Simmons's best interests at heart.
"Teresa is a very lovely lady. She has been a good friend of my brother for over 20 some odd years," Lenny said.
"It stresses me to hear that people think that she is holding him hostage or that she is mean. She isn't. She is a very nice person.
"My brother certainly deserves his vacation. I certainly cannot fault him for wanting to do that.
"I would just hope people [can] be a little bit more respectful and realise that he's worked hard and he still loves people - but he needs some time for himself."
The LAPD also paid a visit to Simmons recently and told People magazine that he is happy and healthy.
"There was something about his housekeeper holding him hostage and not allowing people to see him and preventing him from making phone calls and it was all garbage and that's why we went out to see him. None of it is true," the LAPD's Detective Kevin Becker said.
"The fact of the matter is we went out and talked to him he is fine, nobody is holding him hostage. He is doing exactly what he wants to do. If he wants to go out in public or see anybody he will do that," Detective Becker said.
"He is perfectly fine and he is very happy. I don't know what he is going to do, but right now he is doing what he wants to do and it is his business."
The podcast has been criticised for violating the privacy of a man who clearly wants to be left alone.
The New York Times this week published an op-ed titled 'Missing Richard Simmons': The Morally Suspect Podcast, which questioned Mr Taberski's motives as a "concerned friend".
"As Mr Taberski digs deeper into Mr Simmons's personal life, the question becomes not 'What happened to Richard Simmons?' but 'Is it any of our business?'," The Times asked.
"While Serial [the hit podcast from the creators of This American Life] dug into a serious crime and possible miscarriage of justice, Mr Taberski instead relentlessly pesters Mr Simmons and friends for personal details pertaining to his mental and physical health.
"It's not quite a public shaming; Mr Taberski is careful to express respect for Mr Simmons. Call it a public hounding."