Manchester City are yet to agree compensation with Arsenal that would allow the Gunners to name Mikel Arteta as their new manager.
Arsenal are finalising the paperwork for City's assistant manager, 37, to replace Unai Emery.
Arteta was at Oxford on Wednesday night for City's Carabao Cup quarter-final but it is expected Arsenal will be able to appoint him later this week.
However, City are growing increasingly agitated by Arsenal's conduct.
It is understood there has still not been formal contact between the clubs, with a seven-figure release clause yet to be agreed.
Arteta has kept Manchester City manager Pep Guardiola fully informed of the situation.
A Manchester City source said: "It's surprising to hear that plans are being made by Arsenal to unveil our coach as their head coach on Friday on the basis that no contact has been made by the club to discuss this matter."
Speaking after City's 3-1 win over Oxford United, Guardiola said: "This season he's [Arteta] been with us, we prepare the game as best as possible, before and during.
"I don't have any comment, there is no news. Yesterday I had 48 questions about Mikel, when there's news I will answer it but there's no news.
"I answer the questions, I don't answer any more."