The London club's chief executive Vinai Venkatesham was pictured outside the Spaniard's home following City's 3-0 win at Emirates Stadium on Sunday, which is understood to be the second conversation between Arteta and the Gunners.
City will not stand in Arteta's way should he wish to take the job, however it it understood that the Premier League champions are not impressed with the conduct of Arsenal and will demand a seven-figure sum in compensation should the former Rangers and Everton player leave.
City are unhappy that the London club did not ask for permission to speak to Arteta and are especially annoyed as they played at Arsenal on Sunday and no approach was made when club officials met.
Pep Guardiola's side, however, do not have an issue with the 37-year-old and will allow him to make his own decision.
Arteta played more than 100 times for Arsenal - his final club before retiring - captaining the side.
He joined City's coaching staff in 2016 and is now the red-hot favourite to succeed Unai Emery in the Emirates dugout, with club legend Charlie Nicholas telling Sporting Life Arteta is the right man for the job.
"He is a leader, he has been Arsenal captain before, I like his authority and his passion," said Nicholas.
"This decision would be spot-on and I would be happy to have Arteta. You give him the principles he wants, nail him down and get the gig done.
"They cannot delay this anymore, he must be given it and be given it now, this week."
Sunday's 3-0 defeat to City increased the need for the Gunners to end the uncertainty over the manager's position, leaving the club as close to the relegation zone as they are to the top four.
Interim head coach Freddie Ljungberg replaced Emery following his sacking last month but has won just one of his four league games at the helm, while the club are on a run of just one win from 12 games in total.
