Arsenal star Sanchez looked set to join City as the Gunners lined up a replacement in Monaco’s Thomas Lemar.
But the deadline day deals didn’t go through, leaving City boss Pep Guardiola fuming that he couldn’t land his top target.
And reports in Chile claim City will not let the situation rest.
Newspaper El Mercurio claim City will file a lawsuit against Arsenal over what they believe is the breaking of a gentleman’s agreement between the clubs.
Sanchez had effectively been pledged to City and the club, therefore, didn’t move for another forward as they waited for Arsenal to act on Lemar.
However, the £92million deal for France star Lemar never came off as Arsenal claimed they ran out of time to discuss terms with the player.
City and Arsenal had agreed a £55m deal for Sanchez by midday on Thursday.
El Mercurio claim City may have a case to argue if they can prove Sanchez would have signed the contract offered to him on deadline day.
Sanchez himself has refused to sign a new deal at Arsenal and will now play out the remaining 10 months of the terms – unless he is sold in January.
The 28-year-old is on international duty with Chile and will head back to London next week.