Embattled AC Milan could welcome to the club after reaching agreement with the French international defender's Spanish league side Valencia, reports claimed Wednesday.
Milan are enduring a horrendous start to the campaign having dropped to 12th at 13 points off the pace of Serie A leaders Roma and seen a number of top players join the casualty list.
Defenders Mattia De Sciglio and Ignazio Abate have missed most of the start of the season due to injury.
And although the pair are on their way back from the infirmary, La Gazzetta dello Sport said Milan have reached a "verbal agreement" with Valencia that would see out-of-favour Rami join the Rossoneri in January.
Rami, a central defender who made his name while playing under current Roma coach Rudi Garcia at French side Lille, has been sidelined at Valencia since speaking out against coach Miroslav Dukic recently.
It is believed Milan would sign the 27-year-old French international on a loan deal which included an option to buy.
The report emerges two days after Milan central defender Philippe Mexes, a former France international, was handed a four-game ban for punching Juventus defender Giorgio Chiellini during a 3-2 league defeat in Turin.