The Daily Mirror reports that Spurs are keen to bring in the 21-year-old on loan for the rest of the season.
Morata has started just once in La Liga for Real Madrid this season.
Spurs boss Andre Villas-Boas has reportedly made personal contact to try to convince the youngster to move to the Premier League.
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.