The Austrian is now the current frontrunner despite the internal split between owner Gerry Cardinale and senior adviser Zlatan Ibrahimović over the appointment.
Transfer expert Fabrizio Romano confirmed the meeting took place and that both sides presented their vision to the other at length — covering Glasner's playing philosophy, his approach to squad management, and AC Milan's wider ambition to rebuild completely following the dismissal of Massimiliano Allegri after a fifth-place Serie A finish that left the club without Champions League football.
Romano reported that Glasner was "intrigued" by the scale of the project on offer and by the degree of control he would be given in shaping it. No agreement was reached at the meeting, but both parties are expected to speak again before the end of the week.
Glasner left Crystal Palace after winning the UEFA Conference League, the FA Cup and the Community Shield across two seasons — the most decorated spell in the south London club's history. He is available immediately as a free agent.
Cardinale has been the driving force behind Glasner's candidacy. Ibrahimović, meanwhile, continues to prefer Arne Slot, the former Liverpool manager sacked last Saturday. The internal disagreement has slowed the process considerably with Milan still without a confirmed appointment weeks after Allegri's exit.
Mauricio Pochettino, Xavi and Al-Ahli's Matthias Jaissle remain alternatives under consideration, though none has progressed to the level of engagement that Glasner now represents.