Sky Italia's Gianluca di Marzio is reporting Milan are eyeing Gomez as an alternative to Manchester City defender Manuel Akanji.
The Switzerland international is reluctant to move to Italy and would prefer to remain in England if he must leave City before Monday's deadline.
As such, Milan are lining up a move for Gomez - who is open to leaving Anfield.
The England international, 28, wants regular football at this stage in his career, though whether Liverpool will consider selling so late in the window is another matter.