The Guardian report that the referee, who is facing an FA probe, is angered by the accusation and will deny the claims.
Clattenburg sent off two Chelsea players during their 3-2 defeat on Sunday.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.