ESPN understands Real Madrid are prepared to increase their bid for Luka Modric to £33 million but are unwilling to match Tottenham's £40 million valuation of the midfielder.
Modric's future at Tottenham has been the subject of conjecture for the second summer running, after he was linked with a move to Chelsea last year.
Spurs dug their heels in despite the Blues' interest, yet again their Croatia international is the subject of interest, with Real Madrid favourites for his signature this time around.
Tottenham chairman Daniel Levy is seeking at least £35 million for Modric, with the club uninterested in a cash plus player deal - after it was suggested Nuri Sahin could be used as a makeweight.
Affluent side PSG have also been mooted as candidates for Modric's signature, but it is understood the former Dinamo Zagreb player has his heart set on Madrid.
An ESPN source said: "Real Madrid have now indicated they will increase their offer because they can see that Spurs are not interested in the players in part exchange. Andre Villa Boas has said he is not interested in Sahin.
"Real are back with a bid of £33 million but they do not value Modric at £40 million and in any case they don't have so much money.
"With Daniel Levy insisting the price has to be more than £35 million and close to £40 million this will drag on and maybe Levy will wait until the very last minute before making a final decision."
Modric, 26, was recently fined by Tottenham for not training his team-mates and then failing to attend their pre-season tour of America. He has since apologised for his actions.