Lawyer Lisa Bloom, who represents two of the victims, told Reuters news agency on Sunday she will soon file civil claims, which she said had been held off since federal prosecutors were pursuing sex trafficking charges against the 66-year-old accused.
Another lawyer, Roberta Kaplan, said she hoped to file on Wednesday on behalf of a client. She said her claim will take advantage of a new New York State law, which allows for the pursuit of decades-old cases of abuse.
The Child Victims Act, which takes effect on August 14, gives people a year to sue over allegations of sexual abuse, regardless of when the alleged acts occurred.
Kaplan will sue on behalf of a woman described in the indictment against Epstein as a minor victim.
The unidentified woman was recruited to engage in sex acts with Epstein in 2002 and was paid hundreds of dollars for each encounter with the financier, according to the indictment.
She was 14 when it happened, Kaplan said.
The total amount for the two claims was not made public yet.
A document filed by Epstein's lawyers last month listed his total assets at about $559m, including two private islands and four homes.
One residence, on the Upper East Side of Manhattan, is worth an estimated $77m.
It was not immediately known if Epstein had a will. Several of his criminal lawyers did not respond to requests for comment.
Procedures not followed
Epstein is believed to have taken his own life on Saturday, raising questions around the manner in which he died.
Guards on Epstein's unit were working extreme overtime shifts to make up for staffing shortages the morning of his apparent suicide, a person familiar with the jail's operations told The Associated Press.
The person said the Metropolitan Correctional Center's Special Housing Unit was staffed with one guard working a fifth-straight day of overtime and another who was working mandatory overtime.
The person was not authorised to discuss jail operations publicly and spoke on condition of anonymity.
Epstein was placed on suicide watch after he was found a little over two weeks ago with bruising on his neck, according to the person familiar with the matter.
But he was taken off the watch at the end of July and therefore was not on it at the time of his death, the person said.
The New York Times reported on Sunday that he was left alone in his cell, with guards checking up on the alleged sex trafficker every 30 minutes.
However, sources told The Times that the procedures were not followed on the night of the incident, giving Epstein the chance to apparently hang himself in his cell.
Investigation to continue
Authorities have said the investigation into the sex trafficking and conspiracy charges against him will continue despite his death.
Epstein was taken into custody on July 6 and he pleaded not guilty to charges of sex trafficking that allegedly ensnared dozens of underage girls, some as young as 14.
The alleged offences took place in his homes in Manhattan, New York and Palm Beach, Florida, between 2002 and 2005, according to prosecutors. If convicted, he faced up to 45 years in prison.
Epstein had previously lived a lavish lifestyle, often socialising with powerful people, including princes and US presidents. His arrest had put a spotlight on those relationships.
His most recent arrest also drew scrutiny to a 2008 deal that allowed Epstein to plead guilty to soliciting a minor for prostitution in Florida while avoiding more serious federal charges.
The outcry led Alex Acosta, the then-US labour secretary who as a federal prosecutor helped Epstein negotiate the deal, to resign.