Surveillance footage has shown the Berlin truck suspect travelled through the French city of Lyon by train after the attack.
Anis Amri, 24, was seen on CCTV at the Lyon-Part-Dieu station wearing a cap and carrying a backpack and then on a platform on Thursday, three days after the attack in the German capital.
A French source told the AFP news agency: “A man corresponding to the killer was spotted on the afternoon of Thursday, December 22, on a platform at the station wearing a cap and backpack.
“He appears alone in these images.”
After arriving in Chambery, Amri was then spotted buying a ticket for the fast train to Milan, via Turin, again in cash.
French President Francois Hollande had earlier opened a hospital just hours earlier in Chambery, amid tight security.
Amri was shot dead after he was asked for identification papers and then opened fire on police in Milan on Friday morning.
Police have confirmed he is in the footage in Lyon and that he is also seen buying a ticket for Milan in cash, with a changeover in Chambery.
It is not known how, where or when he entered France.
Last week, British woman Anne Lomax claimed she spotted the Tunisian national in Chamonix, a French resort close to the borders with Switzerland and Italy.
Italian police also said he had been in Chambery, France, before starting his train journey to Milan.
Amri was the subject of a four-day Europe-wide manhunt after he was suspected of hijacking a truck in Berlin and ploughing into crowds of people at a Christmas market, killing 12 people.
Islamic State claimed responsibility for the attack, and released a video last week in which Amri apparently pledges his allegiance to IS chief Abu Bakr al Baghdadi.
German investigators are still looking into whether he had help before or after the attack.