The Croatian midfielder has no intention to remain at Spurs, and it is understood that he informed his current club that he wants a switch to the Spanish champions
The Croatia international is continually being linked with a move to the Liga champions, but both sides have so far been unable to reach an agreement over a transfer fee.
Modric has no intention to stay at Spurs, though, and has reportedly informed Villas-Boas that he has set his sights on a move to the Santiago Bernabeu.
The 26-year-old returned to Spurs on Thursday after an extended holiday following his participation at Euro 2012, and was expected to take part in a training session with his fellow internationals.
However, according to reports, rather than joining his team-mates on the training pitch, Modric visited Villas-Boas to tell the former Chelsea manager of his desire to depart White Hart Lane, while adding that he is "psychologically not ready" to train.
The meeting between the Croatian and Villas-Boas is believed to have lasted for an estimated 30 minutes, before the former Dinamo Zagreb star left the Spurs training facilities again.
Modric is hopeful that the deal will be completed before Tottenham head off to the USA for a pre-season tour, but Villas-Boas intend to take the playmaker with them to the States along with the rest of the squad.