The 31-year-old attacker committed to a new three-year contract with the Gunners earlier this month, putting an end to the speculation that had been growing as his previous deal entered its last 12 months.
Barcelona had been linked with a move for the Gabon international and Aubameyang has admitted they tried to lure him to Camp Nou, but Arsenal boss Mikel Arteta gave him enough reason to remain in north London.
“There were several offers, notably from Barca, but also other clubs," he said on Canal Football Club.
"My priority was to stay for two reasons: the first is the coach, Mikel Arteta, because we spoke a fair amount during the 'lockdown', as they say here, we were at home and spoke several times and he convinced me, notably in terms of the project.
"Of course, secondly, is the love that I receive from the fans and people at the club. Since I have been here I have been treated like one of their own, and as I am one of their own, I am going to stay here, it is as simple as that.”
Reports claim Arsenal are trying to sign Houssem Aouar and have had a €35 million (£32m/$41m) offer rejected by Lyon, who are said to value him at around €60m (£55m/$70m).
Lyon president Jean-Michel Aulas has spoken out on Twitter, saying that the Gunners are not close to meeting his side's valuation.
Aubameyang has admitted that he wants to see his side bring the 22-year-old to the Premier League before the transfer window closes on October 5.
"He's a very good player," Aubameyang said of Aouar. "I hope we will be lucky to have these types of players at the club, I'm sure he can bring a lot to us. I hope he will come even though he's a Lyonnais."
Arsenal have won both of their Premier League games so far this season and will take on reigning champions Liverpool on Monday.
Aubameyang is hopeful that his side can reach the Reds' level and believes they can start with a win at Anfield.
"It would be great to compete with Liverpool. It's going to be a big test on Monday," he said. "We're ready, we're going without fear. Obviously we want to annoy them. It's a dream, and a goal for us."