The north London club are seeking to offload several members of their squad, sources have told ESPN, after spending more than £130million on new players and there had been speculation that the club were willing to listen to offers for their leading striker.
Aubameyang scored a hat-trick on Wednesday as Arsenal thrashed West Brom 6-0 in their Carabao Cup second-round tie at the Hawthorns on the same day Manchester City's pursuit of Tottenham Hotspur forward Harry Kane collapsed.
Sources have told ESPN that City are still in the market for a striker, but when asked at a news conference on Thursday whether he was concerned they could move for Aubameyang, Arteta replied: "I don't know. Pierre-Emerick Aubameyang is our player and he will remain here."
Aubameyang, 32, has scored 64 goals in 115 Premier League games since arriving from Borussia Dortmund for a club-record £56 million in January 2018 but struggled during preseason and missed the start of the campaign after testing positive for COVID-19.
He is expected to start when Arsenal visit City on Saturday but there are doubts over winger Bukayo Saka, who picked up a knock against West Brom, and defender Ben White who has also tested positive COVID-19.
Defender Gabriel is closing in on a return to action following a knee problem as Arsenal seek to kickstart their Premier League campaign following two defeats that have put Arteta under mounting pressure.
"I cannot have more energy, more determination and more desire to turn things around," Arteta said. "I think nobody has that more than myself at the moment."