NHS Greater Glasgow and Clyde says it has been made aware of the cluster and investigations are under way, but neither it nor Police Scotland could confirm the number of deaths.
A problem assessment group involving experts from across health services has met to assess the situation and ensure appropriate early action is taken to minimise the risk of further deaths.
Harm reduction advice has also been issued and people are asked to contact their local GP about further support, including the Inverclyde Alcohol and Drug Recovery Service and
Needle Exchange, both at the Wellpark Centre in Greenock, and Moving On Inverclyde at Kingston House in the town.
A spokesman for Inverclyde Health and Social Care Partnership said: “While the cause of these deaths have not yet been established, we would nonetheless like to remind everyone who uses illicit drugs and their friends and families of the measures they can take to minimise the risk of drug deaths or overdoses.
“We would urge anyone who knows someone who takes illicit drugs to pass the message on to them to be extremely cautious and to follow this advice.
“We are engaging directly with the community through our established networks within Inverclyde and through our partner organisations.
“We will continue to work closely with those groups in Inverclyde and across Greater Glasgow and Clyde to ensure we’re able to care for people within this vulnerable community.”