Spanish radio station Onda Cero say that Real have singled out Thiago, who is thought to be keen on a move back to Spain after leaving boyhood club Barcelona in 2013.
Thiago, 27, played under Julen Lopetegui for Spain and it is believed he could be prised from Bayern Munich for an offer in the region of €50 million.
New keeper Thibaut Courtois was the only bit of transfer business that Los Blancos intended to do this summer, but Golden Ball winner Modric is still angling for a move to Inter Milan.
Though Keita Balde was a relative success in his first season at Monaco, it’s looking increasingly likely that he’s not going to stick around in Ligue 1.
Inter are looking to wrap up a €25 million deal for the former Lazio winger, who scored eight times for Monaco last season after they had shelled out €32m for his services.
Monaco are likely to include a buyback clause for the 23-year-old as well as ask for a loan fee for the first season.
Italian sources, including Sky Italia, claim that Suso’s agent met with Roma’s backroom staff at the club’s training ground on Thursday, with a view to a move in the region of €40 million.
However, any move could hinge on making Diego Perotti a makeweight, whose own representative is also thought to have had sit down talks with the Giallorossi.
Perotti was one of Roma’s better players in Serie A last year but in Suso they would be getting a player six years younger – at 24 – and an incredibly versatile option across the front line.