Officers are appealing for witnesses to a suspicious incident which took place in North Baddesley.
Between 2.30pm and 3.30pm on Friday 21 April two 13-year-old girls were walking along Crescent Road, in the direction of Firgrove Road, when a car described as a silver Ford KA pulled up alongside them.
The driver, an elderly man who they did not know, offered them a lift to the local shop, but they declined.
He has been described as white and aged in his 70s or 80s.
Police would like to hear from anyone who has seen this male, or experienced a similar incident in this area.
PC Helen Mann said: “At this time this is the only incident of this nature we have had reported to us in this area.
“We would ask members of the public not to be alarmed, but to remain vigilant regarding this type of suspicious activity.
“If you saw this incident take place, or have experienced something similar in this area then please call police.
“Alternatively, if you think you can help police identify this man so we can talk to him about this then please get in touch.”
Anyone with information is asked to contact Romsey NPT on 101, quoting 44170148986, or call the charity Crimestoppers anonymously on 0800 555 111.