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 23rd, Amri asked a passer-by where he could catch a train or bus for "Rome, Naples or the south."
Sesto San Giovanni, the town north of Milan where Amri was eventually shot, is the starting point for international coaches to Spain, Morocco, Albania or southern Italy.
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".
Amri had close links to Italy, arriving there in 2011 from Tunisia after the revolution that led to the Arab Spring.
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.
He arrived in Germany in July 2015, amid the chaos of a mass migrant influx, where he went on to frequently change residence and identities.
Then, on December 19th, 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.