The Gabon international was acquired from Borussia Dortmund for a club-record fee of £56 million.
Dembele has failed to make much impact at the Nou Camp since his £135.5 million move from the German side in August 2017 and has been linked away from the side, with the Emirates Stadium one of likely destinations.
However, Keown is of the opinion that a reunion of the former Dortmund stars is unlikely this summer.
“I don’t know, maybe it’s good for the fans,” Keown told Starsport.
“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’s 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 have been back now for four to five weeks.”