A post-mortem examination will be carried out this afternoon after Dylan Donnachie's mother found him dead at the family home in Ayrshire in the early hours of Sunday morning.
The Scottish Sun reported that a pet dog may have played a role in the child's death by climbing onto a couch where he lay sleeping.
The Scottish Ambulance Service said they received a call at 4.32am to a house in Irvine.
An ambulance and a paramedic response unit was sent to the property.
Strathclyde Police said: "Police were called on Sunday to an address in Irvine following the death of a four-month-old baby.
"A post-mortem examination will be carried out in due course to establish the exact cause of death.
"In the meantime, the death is being treated as unexplained."