The Arsenal full back had been linked with a move to the Etihad this summer.
Football Soccer - Spain v South Korea - International Friendly
A report from Spanish media outlet Mundo Deportivo this week claimed that several big European sides were interested in his signature.
Manchester City were among them, with Pep Guardiola keen to add the Spanish international to his squad this summer.
Arsenal's Hector Bellerin in action with Aston Villa's Jordan Ayew
The former Barcelona and Bayern Munich boss is looking to improve both full back positions this summer after assessing the squad he has inherited from Manuel Pellegrini.
As a result he had reportedly had the Arsenal right back monitored, with the player thought be one of the first names considered as a target.
Arsenal's Hector Bellerin and West Brom's James McClean in action
However, according to the Manchester Evening News Arsenal have told City that there is no chance they will be signing the 21-year-old.
They are not intending to lose the right back at any point given he is a key part of Arsene Wenger’s team after establishing himself as a first team star over the last two seasons.
That has caused Guardiola to drop his interest and he will instead focus his attention elsewhere in the transfer window.
Arsenal's Hector Bellerin and Petr Cech applaud fans after the game