Another inmate Metropolitan Correctional Center, where Epstein is being held, has reportedly been questioned about the incident.
The inmate has been named by the media as Nicholas Tartaglione, a former police officer who was arrested in 2016 after being accused of killing four men and burying their bodies.
Tartaglione was reportedly questioned by investigators after Epstein was discovered but denied seeing or touching the other inmate.
The 66-year-old is reportedly now on suicide watch.
Epstein was arrested on July 6 and charged with sex trafficking and exploiting dozens of underage girls in the early 2000s.
If convicted he faces up to 45 years in prison.
The billionaire was recently denied bail on the grounds that he posed a danger to community and there was a high risk he would use his wealth to flee.
He has appealed the decision, asking the 2nd US Circuit Court of Appeals to overturn the rejection of his request to remain under house arrest in his $US77 million mansion on Manhattan's Upper East Side.
Assistant US Attorney Alex Rossmiller said the government's case against Epstein was "getting stronger every single day" as more women contacted authorities to allege he sexually abused them when they were minors.
Mr Rossmiller said last week the government had learned that a raid of Epstein's mansion following his arrest turned up "piles of cash, dozens of diamonds" and a passport with a picture of the defendant but a name other than his in a locked safe.
He also said hundreds, if not thousands, of sexually explicit photos of young women found in his home included at least one purported victim.
Epstein has pleaded not guilty to the charges that have been laid against him.
WHERE TO GET HELP:
If you are worried about your or someone else's mental health, the best place to get help is your GP or local mental health provider. However, if you or someone else is in danger or endangering others, call police immediately on 111.
OR IF YOU NEED TO TALK TO SOMEONE ELSE:
• 0800 543 354 (0800 LIFELINE) or free text 4357 (HELP) (available 24/7)
• https://www.lifeline.org.nz/services/suicide-crisis-helpline
• YOUTHLINE: 0800 376 633
• NEED TO TALK? Free call or text 1737 (available 24/7)
• KIDSLINE: 0800 543 754 (available 24/7)
• WHATSUP: 0800 942 8787 (1pm to 11pm)
• DEPRESSION HELPLINE: 0800 111 757 or TEXT 4202