The approach is unexpected, reports Tuttosport, given Lukaku's history as a symbol of city rivals Inter, where he won the Scudetto and became one of the club's most celebrated strikers. But he is settled in Milan as a city and has been linked with the Rossoneri on several occasions over recent years.
The timing is not accidental. Allegri has been consistent in his demands — he wants a physical, experienced centre-forward capable of making an immediate impact, and has told chief executive Giorgio Furlani and sporting director Igli Tare as much across recent transfer meetings.
Last summer Allegri targeted Dusan Vlahovic, then hoped to land Rasmus Hojlund, and would have accepted Artem Dovbyk. All three fell through. His requirements have not changed.
The primary targets this window are Alexander Sorloth of Atletico Madrid, Nicolas Jackson of Chelsea — currently on loan at Bayern Munich — and Goncalo Ramos of PSG. The Italy international pairing of Moise Kean at Fiorentina and Mateo Retegui, now at Al Qadsiah, are also in the frame. Vlahovic and Robert Lewandowski remain longer-range possibilities.
Lukaku's name is not officially on the list. Napoli are expected to sell him this summer having decided he has not met expectations, and AC Milan are conducting due diligence on all available options rather than ruling anyone out.
For a player who once told Inter he was coming home — and then asked to leave — a move across the city to their fiercest rival would be the transfer window's most striking subplot.