Detectives are leading the probe into schoolgirls being approached in Swindon.
Concerns were raised with the police after two youngsters reported that a man had attempted to engage them in conversation.
Wiltshire Police has not confirmed where the incidents occurred, and people have been warned not to jump to conclusions.
The force said that officers are working to establish the facts and to determine if these incidents are linked and if any offences have been committed.
DS Emma Kinderman said: “We take such reports extremely seriously and understand the concern that reports of this nature can cause.
“However, we would urge people to avoid unhelpful speculation and jumping to conclusions.
“We would ask that members of the public should remain vigilant and report any similar concerns to us.”
Call police on 101 quoting log 54230115639. In an emergency, call 999.
