Keown, who made 310 Premier League appearances for the Gunners between 1993 and 2004, believes the club will opt against making a move for the World Cup winner because of the hefty price tag that Aubameyang arrived for in January, believed to be just around the £60m mark.
Keown said, as quoted by the Daily Star: "I don’t see it happening. It seems like it’s an absolute fortune for the player. It doesn’t look likely.
"But maybe the Arsenal fans are hoping for that sort of marquee signing. I think that work was done last year with Aubameyang."
Aubameyang is reportedly keen on a reunion with former teammate Dembele, with the pair having previously enjoyed a successful spell together at Borussia Dortmund.
Any deal for the French international won't come cheap though, with Barcelona looking to recoup as much of the €105m they paid for the World Cup winner should they sell. The Catalan giants have bought in Malcom from Bordeaux this summer, prompting rumours that they may be willing to negotiate a deal for Dembele.
A deal for Dembele would seem unlikely, with new Gunners boss Unai Emery having significantly strengthened already with five new signings.
Keown is excited for the campaign as a result, believing Gabonese striker Aubameyang could prove to be a star turn: "Aubameyang is going to be a player that I think could really tear up the Premier League this season so we’ll have to wait and see how that happens.
"I think Arsenal will be well prepared because the manager’s had longer to work with his players than everybody else who’s been back to pre-season training."