Corriere della Sera reports the alleged captor told the woman she could be freed upon payment of 50,000 euros (about $A74,245).
Officials have released a mugshot of the suspect, named as 30-year-old Lukasz Pawel Herba.
A picture supposedly uploaded to the organisation's website showed a topless woman tied up alongside details including measurements and nationality in an apparent advertisement - although the image is believed to have been taken from an unrelated pornographic film.
The remote farmhouse where the model was held captive.
Authorities said the kidnappers were going to release her "because she had a 2-year-old child" and their "rules exclude kidnapping mothers".
She was kept handcuffed to a wooden chest of drawers in the bedroom for six days until she was released and taken to the British consulate in Milan.
A statement from Milan police headquarters detailed the woman's ordeal.
According to court documents, the woman was drugged by her abductor and held in a small town in the north-western Piedmont region of Italy.
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He has been charged with kidnapping for the purposes of extortion.
During her detention, Herba had demanded the agent pay $300,000 to avoid the model being sold online though no ransom appears to have been paid, police said.
Officers are now investigating the incident after the man was captured with the model.
Investigations in the case are ongoing in Italy, Poland and the United Kingdom.
But reports in La Stampa alleged Herba had contacted the model's agent and demanded the same £270,000 price for her freedom.
Police said they were not sure if the group actually existed.
The British Foreign Office said only that it is providing consular support to a British woman in Milan and that it is in touch with local authorities.