A talkSPORT report says Gunners boss Arsene Wenger has been strongly linked with the forward, who is being billed as the next superstar forward from Belgian football following in the footsteps of the likes of Christian Benteke and Romelu Lukaku.
The Standard Liege star has bagged 12 goals in 19 league outings in the Belgian Pro League, and the 20-year-old has been mentioned as a target for several Serie A clubs as well as Arsenal.
But the player's agent, Katrien Meire, says there's been no contact with the Gunners over a potential January move.
"Interest of Italian clubs? Some intermediaries have asked," she said.
"Nobody from the Gunners has talked to us - they are just rumours."
Arsenal have been linked with Belgian international Benteke over the past 12 months, but upon signing a new Aston Villa deal his price was considered prohibitive.
The Gunners are still expected to move for a new striker in the January window as they look to provide stronger competition for Olivier Giroud.
The £4.5m-rated Batshuayi would likely be more of a long-term project, although the Belgium under-21 forward is undoubtedly talented.
For now, it looks like Arsenal are just monitoring his progress.