The Tottenham Hotspur playmaker has been a long-term target of Madrid and could finally make the move, according to El Chiringuito TV.
Spurs have so far failed to tie Eriksen down to a new deal, with his current one running out next summer.
Madrid reportedly identified Eriksen's non-commital as a bargaining advantage.
Zinedine Zidane is keen to refresh and reinforce Real's personnel this summer, with Luka Modric now 33 years old.
Eriksen has scored 10 goals and assisted 17 others so far this season, and may yet add more in the Champions League final against Liverpool.
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