The 32-year-old Cahill's fallen out of favor at Chelsea under Maurizio Sarri and admitted in September that he'd "probably" leave if his situation didn't improve. He's made just one substitute appearance in the Premier League since that time, and Sarri seemed to publicly question Cahill's technical ability after excluding him from Thursday's squad for an innocuous Europa League meeting with MOL Vidi.
A report earlier this week suggested Arsenal were considering a move for Cahill following Rob Holding's long-term injury. West Ham United and Southampton are two other outfits understood to be interested in the Aston Villa product.
Cahill joined Chelsea from Bolton Wanderers for £7 million in January 2012, and has since collected two Premier League titles, two domestic cups, and honors in the Champions League and Europa League. He was appointed captain when John Terry left the club in 2017, and represented England 61 times before his international retirement in August.
His experience could be vital for Fulham, who've conceded a league-worst 40 goals this season.
Ranieri, who succeeded the axed Slavisa Jokanovic in mid-November, is also reportedly looking for a right-back and a striker to complement or compete with Aleksandar Mitrovic.