The Sunday Telegraph suggested the inquiry was to abandon examining allegations the former Labour MP abused victims between the 1950s and 1980s.
More than 30 complainants are due to give evidence against Lord Janner, who died in December.
The inquiry has faced various setbacks including the departure of two senior lawyers and three chairwomen.
The newspaper claimed Lord Janner's son, Daniel Janner, a QC, had been told by a source the investigation into allegations his father was a paedophile would be discontinued.
It quoted Mr Janner as saying: "A wholly reliable source has informed me the strand into my father is to be dropped".
But an inquiry spokesman said: "It is not being dropped."
Lord Janner, who was an MP in Leicester for nearly 30 years, died shortly after a judge had ruled that he was not fit to stand trial for alleged child sex offences.
The family believes Lord Janner is innocent and that the 33 men and women who have accused Lord Janner have fabricated their accounts.
The Independent Inquiry into Child Sex Abuse was set up in 2014 to examine whether public bodies, including the police, in England and Wales had failed in their duty to protect children from sexual abuse.
It is investigating claims of abuse involving "well-known people" with one specific strand looking into allegations made against Lord Janner.
The inquiry has seen three of its chairwomen step down in the last two years.
It faced a further setback on Thursday when Ben Emmerson QC, the most senior lawyer working for the inquiry, resigned after saying he was no longer the "right person" for the role.
His colleague Elizabeth Prochaska, the second most senior lawyer on the team, had stepped down on 15 September.
Prime Minister Theresa May has said she still has confidence in the inquiry.
The independent child sex abuse inquiry has denied claims it has plans to drop the investigation into Lord Janner.