Kante has been outstanding since his summer transfer from Caen, and is a nominee for the PFA Player of the Year award, along with Leicester teammates Riyad Mahrez and Jamie Vardy.
The midfielder was recently called into France's international side and even netted in the recent friendly with Russia, and is expected to go to Euro 2016.
PSG have the money to tempt Leicester, and Kante in terms of wages, but they have the players too.
Here is a look at three players Leicester could try and sign in a swap deal...
The Ivory Coast international right-back is so highly regarded that he was forgiven for publicly criticising manager Laurent Blanc on social media, and selected to start a crucial Champions League game against Manchester City. Despite this turnaround, PSG could be convinced that it is best to cut ties, and Aurier, 23, is six years younger than Danny Simpson, who Leicester missed badly when he was sent off against Arsenal.
Benjamin Stambouli has unfinished business in the Premier League after never really getting a chance at Tottenham last season. The defensive midfielder would find his options even more limited at PSG by the arrival of Kante, and getting the chance to prove a point with Leicester. At 25 he has much more to offer, and would be a natural replacement for Kante.
Leicester could really be ambitious here. If PSG want one of their best players, then why not make a play for one of the French champions' most exciting stars? Moura has been at PSG since 2012 but has been overshadowed in the last year by Angel di Maria, and could really shine at Leicester, whose presence in the Champions League could attract him. With Moura on one wing and Mahrez on another, Leicester could become one of the most exciting sides in Europe.