Wiltshire Police has been told of seven incidents in the local area, and PCSOs have been patrolling schools at Church Road, Laverstock and Southampton Road.
So far no offences have been disclosed and police inquiries continue.
Insp Dave Minty asked children and parents to "be sensible" and take proper precautions to ensure safety.
"All of the reports have involved children of secondary school age and these have been only verbal approaches," he added.
"No one has been injured and there has been no attempt to get the young people in the car.
"Nonetheless, we want to remind children to stay safe and report anything suspicious to the police."
The force said local inquiries into the seven reported incidents this month were still ongoing.
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