The Croatian midfielder gave another excellent display as he helped secure Reals third consecutive Champions League title against Liverpool in Kiev on Saturday, having also won the competition five years ago.
However, Marca report that Real are conscious of how important the 32-year-old maestro is to their recent success and are already putting a plan in place for life after Modric.
Bernabeu bosses believe Eriksen – who is six years younger than Modric – is the perfect heir and have been hugely impressed with his recent performanceS for Spurs.
One stumbling block, however, will be Tottenhams desire to keep their Danish string-puller, with Mauricio Pochettino hopeful of convincing Eriksen to sign a new deal.
Real are also wary of getting into a long negotiation with Tottenham chairman Daniel Levy, who drove a hard bargain when Los Blancos signed both Modric and Gareth Bale.
There is no great rush from Real to sign Eriksen, and president Florentino Perez is happy to wait until after the World Cup.
Real supporters demand a certain profile of player and the World Cup is the perfect platform to show off; it was James Rodriguezs displays in the 2014 World Cup that convinced Real to sign the Colombian.
Eriksen could have a similar impact with Denmark in Russia, and Real feel he would inject some much needed quality in the centre of the pitch.
While Reals starting midfielders are world-class, their backups – such as Dani Ceballos and Mateo Kovacic – have disappointed, giving Zinedine Zidane little opportunity to rotate, and those backups could be offloaded to make way for Eriksen.
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