According to Europe 1 radio, Amri passed through Lyon via the Part-Dieu railway station and took a train to Chambery on Thursday, where he bought another ticket to Milan via Turin.
In Chambery, Anis Amri nearly passed by French President Francois Hollande, who was present at the opening of a new hospital in the city, according to Europe 1, which cites surveillance camera footage where the suspect is seen boarding the TGV train.
The radio said that police were too busy ensuring Hollande's security to notice Amri.
On Friday, Italian Interior Minister Marco Minniti announced that Anis Amri had been killed in a shootout with police in Milan early in the day.
The German Interior Ministry considers the deadly Breitscheidplatz square Christmas market attack a terrorist act.