Det Ch Supt Lesley Boal said Police Scotland officers were investigating a historical complaint - but did not confirm a name.
Lord Janner was accused of abuse allegations during the 1960s, 1970s and 1980s - but was deemed unfit to stand trial in England because of dementia.
The former MP has consistently denied all allegations against him.
BBC home affairs correspondent Tom Symonds said the allegation had first been made in 1991 by a Leicester man who told police that Greville Janner sexually abused him during the 1970s - including in Scotland.
Police in Leicestershire investigated allegations against the politician - who represented two constituencies in Leicester between 1970 and 1997 - in the 1990s but no charges were brought, he added.
However Scottish police have reviewed files from the original claim relating to the alleged abuse in Scotland and are now carrying out their own investigation, our correspondent said.
"Because Scotland has a separate and independent prosecutor, it would be able to make its own decision about whether to charge Lord Janner," he added.
In April, the Director of Public Prosecutions in England and Wales, Alison Saunders, decided allegations against the peer by nine men were strong enough to merit a prosecution.
However, she said the prosecution should not go ahead because Lord Janner would to be unable to take part in his defence due to his poor health.
Last month, the Crown Prosecution Service, covering England and Wales, said it would review the decision. A senior prosecutor unconnected to the original case will review the decision.
Justice Lowell Goddard - who is leading an independent inquiry into child sex abuse - has also said she would investigate claims against Lord Janner.

Alassane Ouattara has been in power since his predecessor, Laurent Gbagbo, was forcibly removed from after refusing to recognise Mr Ouattara internationally recognised victory in the November 2010 presidential election.
The poll was meant to draw a line under a 2002-03 civil war which left the country split in two, but it led to a stalemate lasting more than four months.
Mr Gbagbo, who had been in power for 10 years and several times delayed elections, claimed victory in the 2010 poll and held onto power, helped by his militia but isolated by the international community.
Mr Ouattara was initially confined to a hotel near the presidential palace, protected by UN peacekeeping troops.
Eventually his militia overran the country and - together with French troops - stormed the presidential palace and captured Mr Gbagbo in April 2011.
Mr Gbagbo was subsequently transferred to The Hague to stand trial at the International Criminal Court on charges of crimes against humanity.
In 2015, Mr Ouattara won a second five-year term with nearly 84% of the vote, in an election described as credible by US observers. An ally of Mr Ggagbo won 9%.
A US-educated economist from the Muslim north, Mr Ouattara served as President Felix Houphouet-Boigny's last prime minister after a long career at the International Monetary Fund.
After losing a power struggle against Henri Konan Bedie, who became president, Mr Ouattara returned to the IMF, eventually becoming deputy managing director.
He made a comeback in Ivorian politics as head of the liberal Rally of the Republicans, which has strong support in the north, and backed the coup that ousted President Bedie in 1999.
Disputes about whether Mr Ouattara's parents were Ivorian led to his being debarred from standing for the presidency in 2000 - one of the controversies that prompted the 2002 civil war. As part of the post-war settlement, Mr Ouattara was allowed to register for the 2010 election.

Dumfries Sheriff Court was told that the dangerous contraption could have caused damage, a fire or injury.
Tessa Banks, 33, denied making or knowingly having the device in a flat in Queen Street between November 2015 and March last year.
But a jury found her guilty of the charge at the end of a three day trial.
The court heard that the alarm was raised by a friend of Banks, who told police she had been shown the device.
She said she was concerned over what might happen or that someone might get hurt.
A bomb disposal expert travelled from Edinburgh to make the device safe.
Sheriff Brian Mohan deferred sentence on Banks for a month for background reports.
Police in Scotland are understood to be investigating claims Labour peer Lord Janner abused a boy there in the 1970s.
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President : Alassane Ouattara
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A bomb disposal expert called to a flat in Dumfries discovered a homemade device made from three fireworks wrapped in a sock, a court heard.