Everton club scouts watched on as the Nantes forward starred for his club in their 1-0 loss to Lille in France last week. A separate report in French newspaper Le 10 Sport claims Liverpool, Lyon, Udinese and Bologna have all been linked with the Serbian international as well.
Djordjevic will be available on a free transfer next summer, so foreign clubs can talk to him about a move from January onwards.
He's bagged seven goals already this season, attracting attention from across Europe. And Everton, who are already planning for life after Lukaku, have identified the physical target man as a potential replacement.
Toffees boss Roberto Martinez expects the on-loan Chelsea striker to return to Stamford Bridge next summer, so he is already exploring alternatives.
But Liverpool manager Brendan Rodgers was also thought to be interested in the 6ft-1in frontman.
Despite the superb start to the Premier League season enjoyed by Anfield duo Luis Suarez and Daniel Sturridge, Djordjevic would be a completely different option for Rodgers.