Prosecutors have appeared to leave the door open to pressing ahead with criminal proceedings over child sex claims against Lord Janner despite his death.
A "trial of the facts" was scheduled for April to examine charges related to 22 sexual offences dating back to the 1960s against nine alleged victims, mostly under 16 at the time.
Lord Janner's family announced that he had died peacefully at home aged 87 at the weekend.
In a statement, the CPS said: "Greville Janner faced criminal proceedings for child sex offences, with a trial of the facts scheduled to take place in April 2016.
"When a defendant dies during criminal proceedings, it is usual that the case no longer goes ahead following formal confirmation of the defendant's death at a hearing before the court.
"However, we are considering the procedural implications of this specific case."
There can be no hearing before January 11, the statement said, because the High Court closes until that date today.
The CPS added: "It is right that this matter is considered properly in open court, and we will therefore not be commenting further ahead of a court hearing."
A High Court judge ruled this month that Lord Janner's "deteriorating and irreversible" dementia meant he could not stand trial in person.
Director of Public Prosecutions (DPP) Alison Saunders had ruled that Lord Janner should not be charged with alleged child sex crimes because of his ill health.
But that decision was overturned by an independent review in April.
In a trial of the facts, a jury considers the evidence against an individual but there is no guilty verdict and the court cannot pass sentence.
All it can do is make a hospital order, a supervision order, or an order for the defendant's absolute discharge.
Former director of public prosecutions Lord Macdonald suggested that the trial of the facts could still go ahead, although he expressed opposition to such a move.
He told BBC Radio 4's Today programme: "The whole point of a trial of the facts is that it doesn't exist to determine the guilt or innocence of anyone.
"There's no question of a penal sanction at its conclusion. So it doesn't, I suppose, require the presence of the defendant.
"In fact, it only takes place when the defendant is incapable of taking part, as Lord Janner unfortunately was."
He went on: "It is actually quite finely balanced (whether a trial of the facts should go ahead).
"It is a difficult decision yet again for the DPP, I don't envy her. But in the end I think there's something unseemly about a criminal process to determine the acts of a person who has already died.
"That would be a groundbreaking proceeding and, I think, probably groundbreaking in an unfortunate way.
"I think, on balance, I would probably say that the death of Lord Janner is the time to draw a line under all of this."
There have been suggestions that the case could be considered by the independent inquiry into child sexual abuse led by Justice Lowell Goddard.
Lord Macdonald said that in some respects the inquiry "will be a fuller proceeding and a proceeding more likely to deliver full justice than a trial of the facts would be".
Liz Dux, specialist abuse lawyer at Slater and Gordon, who represents six of Lord Janner's alleged victims, said: "My clients' priority is for there to be a judicial finding of facts in this case, be it through the criminal proceedings or via the Goddard Inquiry.
"It is of the utmost importance that such a hearing takes place as soon as possible. If all evidence had been prepared for the trial in April , his alleged victims are asking why this can't go ahead following his death in any event."