Pressure is mounting on the current Gunners boss following a disappointing start to the season, and rumours are suggesting the powers that be at the Emirates Stadium are ready to make a decision.
The 2-2 draw against struggling Southampton on home soil at the weekend was another indication that all is not well at the club and a change could be needed to get the club heading in the right direction.
If Emery was to go, there would be no shortage of top candidates for the job and the like of Carlo Ancelotti have already been mentioned.
However so too has the name of former Gunners midfielder Arteta, who is earning a reputation as one of the best up-and-coming coaches in the game, while under the wing of Guardiola at the Etihad Stadium.
Arteta has been linked in the past, and was touted as a potential successor to Arsene Wenger, but the Arsenal board opted to go with Emery, and he ended up staying with City, winning back-to-back Premier League titles.
Following all the rumours, Guardiola was asked about the future of Arteta, but refused to go too deep into the possibilities of what could happen.
The Spanish tactician admitted it is only a matter of time before Arteta takes a job and becomes a coach in his own right, but hopes it does not happen any time soon.
He also suggested it will not happen midway through a season as City battle for honours at home and abroad.
"I'd like him to stay with us as much as possible," he said. "Manchester City has an incredible, valuable person to work in this club for the future, but personal life is personal life and professional desire is for professionals.
"Everyone, not just me, is more than satisfied to have him here but what happens at the end of the season I don't know."