Witnesses told officers they heard a gun being fired near Anfield Road Primary School at about 09:00 GMT.
Pupils and staff there and at the nearby All Saints Catholic Primary School have been ordered to stay indoors while police investigate.
Ch Supt Mark Harrison said it "beggars belief" it would happen at a school.
Members of the public told police the shot was fired at a dark coloured car by a white man in a grey hooded top who was on foot.
A Merseyside Police spokeswoman said local hospitals had been checked and "no-one has sought medical attention for injuries caused by a firearm".
She said officers were making house-to-house inquiries and studying CCTV footage of the area.
Ch Supt Harrison said the attack "appears to be targeted" and was particularly worrying as "a child could have been seriously injured or worse".
He said police wanted to hear from those inside the car "so we know they are safe".
Anfield Road Primary School's headteacher Clair Drew-Williams said her pupils were "safe and unaware of the incident".
"The site was not evacuated, the school day is continuing as normal and a trip for some pupils took place as planned," she said.
A shot was reportedly fired at a car outside a primary school in Liverpool as parents were taking their children inside, police have said.