The youngster was targeted in a “blatant and repeated” attack in the shop in Bury town centre on the afternoon of 11 September.
She was on the first floor of the shop looking at clothes when a man walked behind and groped her, Greater Manchester Police (GMP) said.
He continued to follow the girl around the store and when she stopped for a second time, she felt her skirt being lifted.
When she turned around she saw what appeared to be a mobile phone in his hand.
The girl ran to find a family member she had gone to the shop with and told them what happened.
The man then reappeared and – not realising the girl’s family member was close by – attempted to approach the her again.
The family member challenged the offender, who “became very agitated and quickly made off through the main entrance,” police said.
GMP have now released an image of a man they want to speak to in connection with the incident.
PC Stephen Raine of GMP’s Bury Division said: “This was a blatant and repeated sexual assault of a young girl when she was simply out shopping with family.
“We are determined to find who has committed this offence.
“We would ask anyone who recognises the man in this picture, or has any information, to get in touch immediately.”