The 23-year-old is wanted by manager Steven Gerrard as the club seek to strengthen their defensive corps.
Bruno Alves is set to complete a move to Parma, which would leave little cover behind summer signings Connor Goldson and Nikola Katic at the heart of the defence.
However, it may prove difficult to lure Cooper from the New Den as Lions boss Neil Harris insists the player is not for sale.
Cooper played 42 times last season as Millwall exceeded expectations to finish in eighth place in the Championship.
He is contracted at the South East London club until 2020.