Wilfried Zaha is also considering joining Cristiano Ronaldo's club Al Nassr after letting his Crystal Palace contract expire.
Al-Nassr and Al-Ittihad have been linked with a move for the World Cup winner amid Kante being yet to put pen to paper on a new deal at Stamford Bridge.
It was earlier reported by transfer expert Fabrizio Romano Saudi emissaries are in London to present an official proposal to Kante and his representatives.
The Chelsea midfielder is out of contract this summer, meaning that he'll be available on a free transfer at the end of June.
Kante missed long spells of the season due to a hamstring injury, but came back into contention in the final weeks of the campaign.
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Asked if he'd like to stay with Chelsea, Kante told Sky Sports last month: "For sure.
"It's an exciting project for the club. Unfortunately this season hasn't been to Chelsea's standards.
"But everyone wants to go in this way, the way of success and winning titles. I hope this club will again fight in this direction.
"Let's see where I will be, but I hope that this is a change for the club, that is most important."
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Meanwhile, Palace icon Zaha has been offered the chance to become the highest paid player in the Eagles' history to extend his stay at Selhurst Park.
Should they make the move, Kante and Zaha would become the latest names to join a Saudi Arabian club with Real Madrid legend Karim Benzema completing a switch to Saudi Pro League champions Al Ittihad.