Diaz, 19, is in the final year of his contract at the Etihad Stadium, and El Chiringuito (h/t Dan O'Toole of the Manchester Evening News) said an agreement is already in place for him to guarantee his services to Los Blancos in 2019.
The teenager joined the Citizens academy from Malaga in 2013 and made his first-team debut in 2016. He scored twice in a 2-0 Carabao Cup fourth-round win over Fulham at the start of November, one of only two senior appearances this term.
Diaz is said to have grown disillusioned with his chances of a first-team future in Manchester and would prefer his odds at the Santiago Bernabeu, where former Castilla coach Santiago Solari was recently appointed manager.
Journalist Kieran Canning cited the same El Chiringuito panel and warned that while the rumour should be treated with caution, there is logic to back it up:
It makes sense the Madrid giants would look for more frugal, young options in the transfer market. Joaquim Piera of Sport wrote that the Brazilian duo of Vinicius Junior, 18, and Rodrygo Goes, 17, had cost a combined €121 million, which is huge even by today's standards.
It's understandable that Diaz, an attacking midfielder and winger by nature, may look at manager Pep Guardiola's ranks and arrive at the conclusion that he'll struggle for opportunities.
Kevin De Bruyne and David Silva can occupy his favoured No. 10 role, while Raheem Sterling, Leroy Sane, Bernardo Silva and Riyad Mahrez offer more than ample competition on the wings.
That's without mentioning Phil Foden, 18 years old and the one City product making genuine impact on the senior team. However, even his prospects don't look too bright, journalist Rory Smith said in January:
Los Blancos have steep competition themselves, but Marco Asensio and Dani Ceballos, both 22, are showing there is space for youth to grow in the club's current setup.
Diaz has long attracted attention in City's youth setup as one of its brightest jewels, but a youngster earning such plaudits also can't be expected to sit on the sidelines so long that it stunts their progress.
Simon Bajkowski of the Manchester Evening News recently pointed out Diaz hasn't necessarily been rewarded for the better work he's displayed this term:
Real could be on to a bargain if they do manage to clinch Diaz's signature on a free transfer, as City seemingly face a fight to convince their starlet to stay next year.