The 21-year-old winger was taken to Camp Nou in an effort to help cover the loss of Neymar to Paris Saint-Germain.
He has found the going tough in Catalunya, with injury issues and questioning of his attitude sparking suggestions that another big-money transfer could be on the cards.
Emirates Stadium is considered to be one possible landing spot and Arsenal have been urged to make a move if an opportunity presents itself.
Former Gunners star Parlour is not overly concerned by Dembele’s troubles at Barca, telling the Daily Star of the World Cup winner: “He’s a quality player.
“He would definitely bring more quality to the team. That’s the sort of player you’ve got to be looking at.
“I think they do look at the background as well - how he would affect the dressing room? Will he knuckle down and work hard?
“That is down to the people who are buying the players now to look into his character. I’m sure they know lots of guys who have dealt with him.
“He’s a quality player so if Emery can handle his personality then he certainly would make the squad better and the team better.”
Dembele was involved in Barca’s most recent outing, as they edged out PSV 2-1 in the Champions League.
Further international recognition also came his way during the last break, but he was unable to guide France into the finals of the UEFA Nations League.