It is not clear what charges justice department special counsel David Weiss plans to file against Hunter Biden.
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A planned plea bargain to resolve tax-and-gun counts faced by the 53-year-old fell apart in July.
That case marked the first time the justice department had charged the child of a sitting president.
The US first son's legal woes have become a political lightning rod as his father pursues a re-election campaign.
On Wednesday, Mr Weiss' office gave a deadline of 29 September for the planned new indictment in a status report required by Judge Maryellen Noreika.
The court filing is related to the felony gun charge alleging that Hunter Biden illegally possessed a firearm while he was a drug user. He is also under federal investigation for his business dealings.
Hunter Biden's legal team responded in a court filing that their client was abiding by the terms of a so-called diversion agreement approved by a probation office, under which he must stay out of trouble for two years.
His attorney, Abbe Lowell, said: "We expect a fair resolution of the sprawling, five-year investigation into Mr Biden based on the evidence and the law, not outside political pressure."
In July, Judge Noreika said she could not approve an "unusual" plea deal overseen by Mr Weiss that would have spared Hunter Biden prison time.
At that hearing, he ultimately pleaded not guilty to two counts of failure to pay federal taxes on income of more than $1.5m (£1.2m) annually from 2017-18.
He was first charged in June.
Although Mr Weiss was a Trump nominee, Republicans have objected to Attorney General Merrick Garland's elevation of him last month as a special counsel to investigate Hunter Biden. They have cited the prosecutor's role in brokering what they regard as a "sweetheart" plea deal.
Mr Weiss' previous working relationship with President Biden's late son, Beau, in Wilmington, Delaware, has also drawn scrutiny.
Congressional Republicans are considering an impeachment investigation of President Biden, alleging that he had played a role in his son's foreign business affairs.
Last month, the House of Representatives oversight committee cited bank records it said showed the Biden family and its associates had reaped $20m from oligarchs in Russia, Kazakhstan and Ukraine during his vice-presidency from 2009-2017.
House Speaker Kevin McCarthy recently said on Fox News: "If you look at all the information we have been able to gather so far, it is a natural step forward that you would have to go to an impeachment inquiry."
