The Croatian star was expected to join the Spanish champions after Euro 2012 but a deal has yet to be done.
Modric, who is valued at £35million, wants Real to make a decision by July 17 or he will explore other options.
Reports in Spain claim Madrid must sell before they can buy and Modric, 26, is reluctant to demand a move away from White Hart Lane, according to The Sun.
Chelsea failed with a bid of £30m for the playmaker last summer as Spurs dug their heels in.
New manager Andre Villas-Boas will be keen to hold on to Modric but has already made plans to replace him.
Gylfi Sigurdsson snubbed Liverpool to join the White Hart Lane club and Lassana Diarra has also emerged as a target.
Spurs will not be held to ransom as Modric's contract runs until 2016 but it remains to be seen if Villas-Boas can convince him his future lies at a club who will not feature in the Champions League.
Source : DailyMail.co.uk
