The girl was walking down Harrison Road at 4.30pm on Wednesday, November 24, when a stranger approached her.
The man, who is believed to be in his fifties, touched the girl’s chest over her clothing before walking towards the nearby Southampton Road junction.
The girl was not hurt, according to a spokeswoman from Hampshire Constabulary.
She said: ‘The man is described as white, aged in his fifties, 5ft 6ins tall, large build.
‘He had short grey, straight hair.
‘He was wearing a navy blue jacket and dark blue jeans.
‘The Neighbourhood Policing Team has been patrolling the area and enquiries have been undertaken to identify relevant CCTV.’
Police have not received any reports of similar incident.
Anyone with information or dash cam footage is asked to call the police on 101, quoting reference number 44210472664, or submit information online here.