Aubameyang was signed by the North London club from Borussia Dortmund for a club-record fee of £56 million in January, while Dembele has been heavily linked with a move away from Barca to join the Gunners in recent weeks.
Keown believes Dembele will not join the Gunners because Arsenal already signed Aubameyang in January this year.
He urged the Arsenal’s fans not to expect Dembele at the Emirates stadium.
Speaking on the possibility of Dembele joining Arsenal this summer, Keown told Starsport: “I don’t know, maybe it’s good for the fans.
“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 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.
“It’s great because in a week’s time all the talking stops and we’ll see who’s the best.
“I think Arsenal will be well prepared because the manager had longer to work with his players than everybody else who’s been back to pre-season training.
“You look at the number of players that still aren’t back properly, Arsenal have had that advantage that the core of the players has been back now for four to five weeks.”
Arsenal will be hoping to kick star their Premier League campaign on high when they tackle Premier League champions, Manchester City this weekend.