The former Manchester United star is out of contract at the Groupama Stadium this summer and appears set to depart Les Gones, with Barcelona showing an interest in him.
However, the Spanish club are in danger of losing out on the Netherlands international, according to Calciomercato.com, with Juventus stealing a march to become the favourites for his signature.
With Barcelona facing an economic crisis, the Blaugrana may be unable to match the wages on offer at Juventus, and the opportunity to sign for the Bianconeri is thought to be a proposition Depay is keen on.
Meanwhile, Bundesliga outfit Dortmund are also in the hunt for Depay, though Juventus have overtaken them as the most likely destination for the 27-year-old.
Depay joined Lyon from Manchester United in January 2017 and has gone on to score 68 goals in 164 appearances for the Ligue 1 club.