Shkreli's lawyers, in a letter to U.S. District Judge Kiyo Matsumoto, requested on Tuesday that the judge recommend the camp at the Canaan Federal Penitentiary near Waymart, Pennsylvania.
The camp, adjacent to a much larger high-security prison in the state's northeastern corner, houses 107 inmates.
While Matsumoto can make such a recommendation if she so chooses, the decision is up to the federal Bureau of Prisons.
And it's not clear that Shkreli, 34, could get to do his time for securities fraud in a minimum-security prison with other nonviolent con artists and white-collar crooks.
At Shkreli's sentencing Friday, defense lawyer Benjamin Brafman told Matsumoto that her ruling in September revoking his $5 million release bond could prevent Shkreli from being sent to a low-security, and hence potentially much safer prison.
Matsumoto, in revoking Shkreli's bail, had found that he represented a danger to the public because of his bizarre offer of a $5,000 bounty for each follicle of hair that his Facebook followers could grab off the head of former Secretary of State Hillary Clinton.
That finding, Brafman said, could effectively force Shkreli to do his time in a higher-security prison, where he would be much more likely to come into contact with inmates who have a history of violence.
Brafman said Shkreli, who broke down in tears before being sentenced, has been locked up since last fall in a federal jail in Brooklyn. It's a maximum-security facility where he has witnessed violence and has become concerned about his personal safety.
Matsumoto asked Brafman at the sentencing if he planned to request that she void her finding that Shkreli represented a public danger. Brafman said he would be doing so.
If Shkreli does not win such a request, he risks going to tougher prison, such as the high-security facility at Canaan, which houses nearly 1,500 inmates. The prison has had four slayings since 2010, with victims including a prison guard and a Mafia associate who was stabbed 92 times.
The high-security facility was also the scene of an outbreak of salmonella that sickened 300 or so inmates who had eaten tainted chicken.
Brafman did not immediately return a request for comment Wednesday from CNBC.
Shkreli repeatedly lied to investors in the funds about the strategy, oversight and performance of those funds.
And then he used stock shares and cash in Retrophin to more than pay back the investors the money they had lost with his funds. He also manipulated Retrophin's stock illegally, a jury found.
Shkreli cried Friday in Brooklyn federal court as he asked Matsumoto not to give him a harsh prison sentence.
"The one person to blame for me being here today is me," Shkreli sobbed. "Not the government. There is no conspiracy to take down Martin Shkreli."
"I took down Martin Shkreli with my disgraceful and shameful actions."
"This is my fault. I am no victim here," he said.
With credit for time served, as well as for good behavior in prison, Shkreli could be released in less than 5½ years.
Matsumoto also has ordered that Shkreli forfeit nearly $7.4 million to the federal government and pay a $75,000 fine.
To secure the forfeiture amount, Matsumoto ordered Shkreli to give up his ownership rights to a group of assets that include $5 million in cash in an E-Trade brokerage account that previously had secured his release bond; his stake in the drug company Vyera Pharmaceuticals; the one-of-a-kind Wu-Tang Clan album "Once Upon a Time in Shaolin"; the Lil' Wayne album "The Carter V"; and a painting by Pablo Picasso.
Privately held Vyera was originally known as Turing Pharmaceuticals, which Shkreli founded in 2015. He gained notoriety that year for using Turing to buy the rights to the anti-parasite drug Daraprim, whose price he promptly hiked by more than 5,000 percent.
The crimes that Shkreli later was charged with were not related to his tenure at Turing.
Shkreli plans to appeal his conviction.