The French publication claim that Stoke put forward a huge written offer for the striker yesterday, yet Marseille have turned it down as they believe they can potentially sell him for more this summer.
The 22-year-old has dominated the headlines in France this season, putting in a number of good performances and attracting the attentions of a host of top-level clubs.
With 12 goals and seven assists in 22 league matches to his name, Batshuayi has become the subject of intense interest from the Premier League as clubs eye up his lethal goal scoring ability.
Tottenham Hotspur and Newcastle United are also mentioned as strong suitors in the report, with the Magpies in particular in the hunt to secure a new striker before the deadline.
Yet it is Stoke who have pushed to the front of the queue, submitting an offer and hoping to lure the striker to the Britannia Stadium in the way that Bojan Krkic and Xherdan Shaqiri surprisingly joined the club.
The Potters have established themselves as a top Premier League side this season, and with a bit more firepower upfront, a push for a top four place could become a realistic objective.
Mark Hughes is intent on raising the profile of the club, and with heavy financial backing there appears to be no limits as to how far the Staffordshire club can really go.
Batshuayi would be a fabulous addition, though for now he appears off-limits until the summer.