The Sun says Real will make a late £60million bid for Eriksen.
But the Spanish giants are waiting until the last minute to pile pressure on Tottenham chief Daniel Levy to accept a 'take it or leave it' offer for the Dane.
Spurs chairman Levy is determined not to let big assets leave on a free and sold Mousa Dembele last season rather than allow him to run down his contract.
Madrid aim to use Levy's policy to their advantage over Eriksen — who they see as the successor to Luka Modric.
There is confidence at the Bernabeu they can snatch Eriksen just before the European transfer window shuts on September 2, especially as the playmaker has just 10 months remaining on his Tottenham deal.