The newly promoted Scottish Premiership side are still looking to build a squad suitable for their return to the top flight, after a 1-1 draw on their first game back against Hamilton.
The 34-year-old, who has been capped 5 times by France, was sent out on loan to Charlton Athletic last season, and is considering a move to Scotland. However, his former side Marseille have also offered Fanni a deal, putting a 1-year contract on the table for Fanni.
Rangers have already made 9 summer signings, but Mark Warburton is keen to continue building his squad, and is rumoured to be keen on Fanni according to the French reports.
Fanni was a Marseille player between 2011-2015, making over 125 Ligue 1 appearances for the club, winning the Coupe de la Ligue twice. He is currently signed on at Qatari side Al-Arabi SC, but made 14 loan appearances for Charlton last season.