It would see new boss Claudio Ranieri looking back towards his former club, who he managed between 2012 and 2014, getting them promoted back into Ligue 1.
Tisserand was a youth prospect at the time, still just 22-years-old, but was handed his debut by Ranieri back in August 2013.
He has since been out on loan at Lens, and last season at Toulouse, with competition for places at the Champions League side making it tough to break through.
Tisserand is a right-back, but is versatile enough to play across the back four, and could be a smart addition for Leicester given Ranieri's knowledge of him.
The interest has progressed already but is no certainty. Tisserand's agent Patrick N’Tanda told The Times: "We are in advanced discussions with Leicester but we are not on the verge of signing anything. Monaco do not want to let Marcel go at the moment."
Tisserand has made just six first team appearances for Monaco, last season playing 22 times for Toulouse, providing one assist.