The Gunners are in the hunt for a new manager following the sacking of Unai Emery and it has become clear that current interim boss Freddie Ljungberg will not be getting the job long-term.
Arteta was heavily linked before Emery was appointed to replace Arsene Wenger, and reports linked him again as soon as the job became vacant again.
Speculation linking the City assistant coach with the vacancy at the Emirates Stadium has intensified further after pictures emerged of Arsenal managing director Vinai Venkatesham outside Arteta's house in the early hours of Monday morning.
However, reports claim the Premier League champions are not impressed with the conduct of Arsenal and will demand a seven-figure sum in compensation should the Spaniard leave.
It is understood two meetings have now taken place and City are unhappy that the London club did not ask for permission to speak to Arteta.
They are especially annoyed because City played at Arsenal on Sunday, when they ran out comfortable 3-0 winners, and no approach was made when club officials met.
Despite City being angry with the Gunners, they do not have an issue with 37-year-old Arteta, and will allow him to make his own decision.
Should that decision be to take the Arsenal job, then he will be allowed to leave with City's blessing, but it is fair to say relations between the two clubs have become strained and Christmas cards will not be exchanged.
It was initially thought that Arteta may want to hang around until the end of the season as City push for more honours, but the chance to take the Gunners job and be a coach in his own right looks too good to turn down.