The girl was approached by a white van in Beech Ride at around 2.40pm on Wednesday, January 15 when the passenger reportedly spoke to the girl.
The passenger, a white man in his late 20s to early 30s wearing an orange jumper, offered the 12-year-old sweets. She did not respond to the man, instead walking away.
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The van drove away from the area.
Officers from Hampshire Constabulary said that since the incident they have been carrying out a number of enquiries and are now appealing for witnesses.
Fleet Police Sergeant Geoff Hill said: “We know this incident may be concerning to the local community, however, I would like to reassure you that we are taking this report seriously.
“We have been carrying out regular reassurance patrols in the area and anyone with information which could help our enquiries should get in touch with us.
“I would urge residents to continue to report incidents to us as soon as they happen as it enables our teams to respond accordingly.”
A spokesperson for the force added: “Anyone with information is asked to call 101, quoting the reference number 44250022463.
“Alternatively, go online and submit information via hampshire.police.uk/tua/tell-us-about/cor/tell-us-about-existing-case-report/”