Pep Guardiola has refused to comment on Arsenal's conduct over the appointment of Mikel Arteta as their new boss.
Arteta's three-and-a-half-year spell as Guardiola's assistant came to an end on Friday afternoon when Arsenal announced the 37-year-old as a permanent replacement for Unai Emery.
City, however, were not impressed with the manner of Arsenal's pursuit of Arteta, the PA news agency understands.
Arsenal managing director Vinai Venkatesham was pictured outside the Spaniard's house in the early hours of Monday morning, before the Gunners made a formal approach to City, while no-one from the Arsenal hierarchy mentioned their interest in Arteta to any of their City counterparts during last Sunday's match at the Emirates Stadium.
"We'll have to see altogether how it works, what is going on. I've said many times how incredibly good it is for me here and of course I would like to stay as much as possible.
"So that is my desire, but I want to be sure this is the best for the club, that they want me to stay longer.
"It would be five years at one club and in this competition that is many, many years, so that's why it's better to be sure your decision is perfect for both sides.
"There's no rush. It's not finishing in three or four months and the club is working perfectly in all departments, so it's not a problem, honestly."