A 28-year-old man has been arrested in Dudley, after a mother and her nine-month-old son were found dead at their home in Billesley, Birmingham on Sunday morning.
ITV reports that the victims are thought to be Yvonne Walsh and her son Harry.
Police were called to the address after neighbours became concerned about the safety of those in the property.
Sky News reports that there had been 'previous contact between police and the person in custody' and that a West Midlands Police spokesman said a serious case review and a domestic homicide review are likely to be carried out.
Superintendent Jo Chilton said: "This is a terrible crime and my thoughts are with the family of the victims who have been left devastated by today's events."
"We have a man in custody and are not looking for anyone else, but I am keen to speak to any witnesses or anyone who may have seen anything which could assist our investigation."
West Midlands police said they are not looking for anyone else in connection with the deaths, and that a post-mortem will be carried out to establish exactly how the mother and baby died.
Superintendent Andy Shipman told Sky News: "Today's awful murders will of course send shock waves through the community. My thoughts are with the family of those involved.
"I want to reassure the community that a man has been arrested and we believe there is no ongoing threat to the public."
The arrested man is reportedly being held in a secure facility after an assessment by mental health professionals.