Zinedine Zidane oversaw a major summer rebuilding process which saw the likes of Hazard, Luka Jovic, Eder Militao and Ferland Mendy signed for a combined total of over £300million.
Despite a near unprecedented level of investment, Real have started the new campaign in indifferent fashion, drawing two of their opening three La Liga games and failing to keep a clean sheet.
Zidane maintains a long-term interest in Manchester Uniteds Paul Pogba, while at least one of PSG duo Kylian Mbappe and Neymar are likely to be available for purchase next summer.
But, according to The Atheltic, ex-Chelsea duo Courtois and Hazard have confided in friends that Kante should represent their managers priority target.
Zidane remains heavily reliant on the midfield trio of Toni Kroos, Luka Modric and Casemiro which led Real to three successive Champions League titles before the Frenchman stepped down in the summer of 2018.
Dani Ceballos is likely to return next summer after a 12-month loan stint at Arsenal but Kante, regarded as the worlds best defensive midfielder, would offer the sort of protection the Spanish giants appear to be in desperate need of.