Arsene Wenger was credited with an interest in Thauvin earlier this summer, but the 20-year-old winger eventually joined Marseille.
Wenger scouted him first when he was still at Bastia last season, before a move to Lille in January didn't work out. And he joined Marseille without playing a game for the northern French Ligue 1 side this summer.
The report claims Arsenal will consider a bid in January, although a summer switch could be more likely.
Arsenal fans will get the chance to catch a glimpse of Thauvin first hand on Wednesday night, as the Gunners face Marseille in the Stade Velodrome in the Champions League.
The 20-year-old attacker featured for the French under-20 team earlier this summer at the under-20 World Cup. And Thauvin was one of the most impressive performers, scoring three goals in seven appearances as France won the competition.
Arsenal travel to the south of France for their first Champions League group stage match of the season this week.
And Wenger will be looking to get off to the best possible start with tricky games to come against Napoli and Borussia Dortmund.