The Corriere della Sera daily said that security cameras at Turin station had twice recorded the 24-year-old searching for trains either to Rome or Milan.
"In the end, he chose a regional train for Lombardy because at that late hour, there was no train going to the capital," said the paper, adding that this showed he had "no precise travel plan."
Several papers also reported that when he arrived in Milan in the early hours of December 23, Amri asked a passer-by where he could catch a train or bus for "Rome, Naples or the south."
Local Rome daily Il Messaggero said it was "not a coincidence" that he was eyeing the capital as that city was where he "probably had the most contacts".
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While in Italy, he served a four-year sentence for setting fire to a refugee shelter -- a prison stint during which he was radicalised, security sources believe.
Then, on December 19, he is thought to have driven a hijacked truck into a crowded Christmas market in Berlin, killing 11 people and also shooting dead the registered driver, a Polish man.
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