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.
Police in Scotland are understood to be investigating claims Labour peer Lord Janner abused a boy there in the 1970s.