Eriksen admitted his desire to seek a new challenge earlier this month and he has been heavily linked with a switch to the Bernabeu.
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His hopes of joining Real have recently been handed a boost as Paul Pogba, who is a key target for the LaLiga outfit, will only be allowed to leave Man United if a huge £150m bid is made for the Frenchman.
Spurs value the Dane at £100million despite him having only one year left on his contract at the Tottenham Hotspur stadium.
And, according to The Times, family members of the 27-year-old are house hunting for properties in the Spanish capital ahead of a proposed move.