The teenagers, who are aged 14 and 15, were arrested in the northern city of Busto Arsizio, after they were caught shoplifting clothes at a shop in the centre of town.
According to Tgcom24, one of the teenagers managed to escape after stealing a T-shirt from a shop from which he had removed the security tag. The other two were arrested at the shop where they were found to be wearing stolen T-shirts and trousers.
Police then discovered bags belonging to the two teenagers in the shop which they had left nearby. Inside police found more stolen items, including a jacket, snacks and pregnancy tests that they had robbed from a supermarket earlier that day.
The first teenager was tracked down and the three were taken in for questioning by police, where they made the audacious request for a selfie with police officers as a souvenir of their first arrest.
Perhaps unsurprisingly, police did not grant their request. The three face charges for shoplifting.
This isn't the first inappropriate selfie to hit headlines in Italy this past year.
In January the president of Serie A side Roma, James Pallotta, hit back at Lazio counterpart Claudio Lotito in a row over a selfie picture taken by Francesco Totti during the sides' 2-2 derby draw.
Although it created hype on social media around the world, Lotito said Totti's gesture was misplaced.
"It would have made sense after the game, not during it. My captain would never have done the same," he said.
And in October last year an Italian nurse being investigated for the deaths of some 87 patients in northern Italy sparked revulsion when photos were released of her grinning next to dead patients.