Shortly before 1.40am on Sunday, 16 October 2016 police were called to Hilton Lane in Worsley.
On arrival officers discovered damage to a window which was consistent with a shotgun discharge.
House-to-house enquiries were carried out and extra patrols have been taking place in the area.
Detectives now believe the shooting was a case of mistaken identity.
Detective Inspector Ben Cottam, from GMP’s Salford borough, said: “Following extensive enquiries, there is nothing to indicate why this house was specifically targeted.
“We believe the offender has mistakenly shot at this house, frightening an innocent family in the process.
“I cannot stress enough how serious this could have been as two children were asleep in the room at the time of the offence.
“We are continuing to follow enquiries and are doing everything possible to find the offender.
“Again, I would urge anyone with any information to please contact police.”
Information can be passed on to police by calling 101. Alternatively, if you wish to remain anonymous you can call 0800 555 111.