The centre-back’s deal with the San Siro giants is due to expire at the end of the current campaign and a renewal seems highly unlikely.
According to La Repubblica newspaper, the ideal destination in his mind is Lazio, because although Romagnoli spent time in the Roma youth academy, he has never disguised the fact he supports the Biancocelesti.
The Aquile are also seeking a new defender to bolster the options for coach Maurizio Sarri and his switch to a 4-3-3 formation.
La Repubblica claims the 26-year-old will gladly wait to join Lazio as a free agent next summer, but it could suit both clubs and player to make the deal stick in January.
Milan paid €25m to sign him from Roma in 2015, after his loan spell with Sampdoria.