The French centre-back spent the latter half of last season on loan at the San Siro from Valencia after falling out with coaches and members of staff at the Mestalla.
Even though he has been impressive in Serie A, Los Che are thought to be unwilling to bring him back this summer, opening the door for a full move.
Milan are understood to be keen to make Rami’s stay a permanent one, but now Arsenal are ready to enter the battle.
The Rossoneri can snap up the defender for as little as £5.5m, yet are trying to push that figure down further still in the knowledge that the player has no future at Valencia.
Reports suggest Arsene Wenger is more willing to match his price-tag, opening the door for a move.
Rami may be used as a replacement for out-of-favour Belgian Thomas Vermaelen.
As well as Arsenal, Marseille are thought to be interested.