The 30-year-old Sevilla centre-back shone for Les Bleus at EURO 2016 after being drafted into Didier Deschamps’ 23-man squad following Mamadou Sakho’s ban and Raphael Varane’s injury woes.
Rami helped France all the way to the final in Paris, but was forced to sit out his nation’s loss to Portugal due to being banned.
However, he sufficiently impressed Leicester along the way, with reports claiming that Claudio Ranieri’s side are keen to lure him to the Premier League.
Rami starred for Unai Emery’s Sevilla as they beat Liverpool in the Europa League Final last season, but with the coach having moved on to join Paris Saint-Germain, the futures of certain stars at the Ramon Sanchez Pizjuan are unclear.
Leicester are seemingly keen to add the experienced ex-AC Milan man to their ranks as they prepare for Champions League football, with Robert Huth and Wes Morgan short of cover heading into 2016/17.