Reports suggest Diaz has agreed a £60,000-a-week contract with the European champions, who have, crucially, guaranteed him a spot in the senior squad.
City are reluctant to lose the 19-year-old but understand why the Spaniard is attracted to Real, together with his view that the competition offered by Riyad Mahrez, Leroy Sané and Raheem Sterling means playing regular football at City is hard.
The reigning Premier League champions may not be able to keep Diaz, but they surely don't want him playing against them.
Diaz will be presented to local media and fans on Monday at the Santiago Bernabeu.
City have also included an agreement whereby they would receive 40% of any future transfer fee if Diaz were to join Manchester United.
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However, the Blues have now accepted that Diaz, a Spain Under-21 worldwide, will join Real Madrid for a fee that could rise to £21m.
However, the versatile attacker has not added to his five Premier League substitute appearances this term and the prospect of greater first-team opportunities at Madrid is understood to have been a motivating factor in his decision to leave the Etihad Stadium.
Pep Guardiola's side made sure to include a buy-back clause in the winger's deal meaning they can re-sign Sancho in the future.
Meanwhile, Madrid remain fifth in LaLiga after their lacklustre campaign continued with a 2-0 defeat at home to Real Sociedad that increased pressure on boss Santiago Solari.