The 28-year-old – a former Liverpool target – has spent the latter half of the season on loan at AC Milan from Valencia after falling out with senior members of staff at the La Liga club.
Despite the months having passed since January, the Spaniards are rumoured to be unwilling to bring the centre-back back to the club, opening up the possibility for a move.
Valencia are understood to have slapped a £7m price tag on the former Lille man, which may deter Milan with the player himself entering the final year of his contract.
However City and Arsenal can easily afford to match such a sum, and may look to lure him to England.
Arsene Wenger is known to be a big admirer of the defender after being linked with him on numerous occasions, while the Sky Blues are thought to be ready to snap up a top-class enforcer to partner captain Vincent Kompany at the heart of their backline
Yet both clubs might be wary of moving for Rami, who has endured a long line of high-profile bust-ups with previous clubs.