OM had been tracking Kante at SC Caen for 18 months ahead of moving for him last year.
However, RMC says while OM were confident of a deal, they were blown out of the water by the Foxes.
"It was a wage battle. Leicester offered triple (the money) to Kanté compared to OM," reported Mohamed Bouhafsi of RMC.
Kante has been one of the big revelations of this Premier League season at Leicester.