Juventus have held a long-standing interest in the former Chelsea striker, who has scored 50 Premier League goals since arriving on Merseyside in 2013.
However, the Serie A giants will face competition should they wish to sign him as, according to reports in France, PSG want him in the French capital.
The Ligue 1 side lost Zlatan Ibrahimovic to Manchester United during the summer and they now wish to ease the striking burden on Edinson Cavani in attack.
And Le10Sport has claimed that, despite interest in the likes of Carlos Bacca, it is Lukaku who tops their wish list.