The duo were among the Real Madrid stars to face abuse while returning home on Monday and those responsible could be made to pay €3,001
The supporters who attacked the cars of a number of Real Madrid players including Gareth Bale and Jese Rodriguez are facing potential fines of €3,001.
Three fans, infuriated at Real Madrid's 2-1 defeat by La Liga leaders Barcelona, waited for players to leave the club's training ground in the early hours of Monday and proceeded to punch and kick their vehicles as they drove away.
Head coach Carlo Ancelotti also suffered a barrage of verbal abuse upon his exit from the Valdebabas after the Clasico and, after footage of the fans' hostility emerged, the European champions responded by banning a club member and encouraged the Anti-Violence Commission "to implement the sanctions deemed appropriate".
The CSD have suggested fines of €3,001 for three of the fans and banning orders that would see them denied access to sporting facilities, such as stadiums or training grounds, for up to six months.
Real Madrid will be hoping to appease fans - many of whom have become frustrated with losing their lead in La Liga to Barcelona - when the international window ends next weekend.
The Blancos have matches against Granada, Rayo Vallecano and Eibar to look forward to in the coming weeks.