It is alleged that Lord Janner sexually abused a boy after travelling to Scotland with him. The alleged victim complained to police in Edinburgh in 1991 but Scottish prosecutors say they were never told of the case.
Following the CPS decision in April, Scottish detectives are said to have trawled files for details of the 1991 claim.
A senior officer at Police Scotland confirmed officers were investigating an historical complaint.
Lord Janner, who has held numerous communal leadership roles over the past six decades, has repeatedly denied any wrongdoing.
His lawyers and family said in a statement after the CPS decision that he was "a man of great integrity and high repute with a long and unblemished record of public service".
A lawyer representing alleged victims said civil claims against him would be pursued regardless of the actions of prosecutors.
An independent QC is reviewing the CPS decision, and lawyer Liz Dux said she would pursue a “series of individual claims” on behalf of alleged victims once the review was complete.
