Arsene Wenger had also pushed for a move for Bordeaux forward Malcom in attempt to soften the blow of Alexis Sanchez leaving for Manchester United, though a deal for the Brazil Under-20 star failed to materialise.
Aubameyang has scored 13 goals in 15 league starts this season for Dortmund after 31 in 31 last term, but former Gunner Petit believes that it'll take more than the Gabon international to transform the club into Premier League title candidates.
“There has been a lot of speculation about the likes of Pierre-Emerick Aubameyang and Malcom coming in – but Arsenal should be aiming higher,” he told the Metro.
“Because they are not competitive on the pitch at the moment, they need to be more competitive with wages.
“If you can’t guarantee trophies – or at least compete to win them – then you must offer players more in order to come to the club. That’s the way it works.”
Arsenal are also on the verge of completing a deal to bring Manchester United's Henrikh Mkhitaryan to the Emirates, having missed out on the Armenian before his move to United in 2016.
Wenger remains a fan of the 28-year-old and is keen to reunite him with Aubameyang at the Emirates before the end of the month, with the club's new head of recruitment, Sven Mislintat, heavily involved in the moves.
Mislintat, who arrived from Dortmund in November, has played an integral part in the transfers and has referenced his experience spent working with them at Westfalenstadion as reason to pursue both players in the January transfer window.
Again, though, Petit isn't sure whether Mkhitaryan is the man Wenger should be signing, comparing his lacklustre work-rate to that of Mesut Ozil's.
“Since he signed for United, he hasn’t been involved enough, and I’m not sure he has a winning mentality," he added.
“Sometimes he reminds me of Mesut Ozil – you really have to push him to show his character, and put him under pressure to display his best qualities.
“There’s no doubt he has great skill, but I’m not sure he’s the kind of footballer Arsenal need. They should be focussed on other positions.”