The Spanish champions have been chasing the Croatian international all summer but have yet to match the £40million asking price Spurs chairman Daniel Levy is demanding for his signature.
New boss Andre Villas-Boas has frozen Modric out of his pre-season plans after the playmaker refused to travel to the United States for the clubs tour in an effort to force through a move to the Bernabeu.
But with Levy unflinching in his demands and Jose Mourinho reluctant to meet the North London clubs valuation the Madrid coach is now expected to abandon his pursuit of the 26-year-old.
Instead he is expected to target Dembele following his emergence as a top Premier League midfielder last season and has long been linked with a move away from Craven Cottage since arriving from AZ Alkmaar in a £5-million deal three years ago.
Manchester United, Spurs and Chelsea have all been credited with an interest in the Belgium international after his impressive displays for the Cottagers last term in the wake of his switch to the centre of the park.
His performances are said to have caught the eye of Mourinho who is now said to be mulling over an approach for the 25-year-old despite manager Martin Jol’s desire for him to remain in West London.
However Dembele has already confirmed that his agent has spoken to the La Liga giants regarding a possible move but refused to divulge more information although it’s thought no firm offers have been submitted.
“I do not know (if I will leave),” he told Het Nieuwsblad. “Actually I can say nothing about.
“There was contact between Real and my agent. They wanted information, but that was it. Everything is still.”