Retired GP Dr Iain Kerr revealed he had prescribed particular drugs and gave advice to patients who wanted to end their own lives.
Dr Kerr, who worked at Williamwood Medical Centre in Clarkston, East Renfrewshire, has previously been interviewed by the procurator-fiscal, who took no further action.
The 66-year-old said he would be happy to co-operate with further police investigations.
A Crown Office spokesman said: "We have instructed police to make inquiries into whether there is any new evidence available. Any new evidence will be considered by Crown Counsel. There is no crime of assisted suicide in Scotland, where, depending on the facts and circumstances, the law of homicide may apply."
Dr Kerr was suspended for six months in July 2008 after appearing before the General Medical Council on charges including prescribing sleeping tablets to a patient so she could end her life. In 2010, all restrictions on him practising with NHS Greater Glasgow and Clyde were removed by the GMC.
MSP Margo MacDonald, who is preparing a Holyrood Bill allowing registered individuals to help people with a terminal illness end their lives, said Dr Kerr is "brave and caring".