According to the reports, a van driver approached the three schoolgirls near Portobello High School and was "staring intently", leading them to run away.
The incident reportedly took place on a street next to the school around 2.15pm yesterday.
The three girls, who are of S1 age, were heading home via Park Lane when one noticed a white van drive passed them, before reversing and stopping next to them.
According to the reports, the driver had a white dog in his lap and was staring at the girls, who ran to one of the parents' homes nearby.
One parent told Edinburgh Live: "When they arrived at our house my daughter hammered on the door shouting, 'let us in,' and looked absolutely terrified.
"When they told me what happened, I phoned the police on 999 and they immediately went to see if they could find the van before coming to our house, they arrived within 30 minutes."
She said a similar incident involving a man in a white van with dogs had been reported in the same area last year.
A Police Scotland spokesperson said: "Enquiries are ongoing."
However, at this point, no criminality has been established.