As reported by The Sun, the 27-year-old is into the final year of his contract at the Emirates Stadium, which could see the club cash in on the Welsh international in order to bring Dembele to London.
The article also claims that Barcelona would only be willing to let the 21-year-old World Cup
winner leave the Nou Camp if Ramsey is included in a deal, which could now happen after the Catalan club recently signed Brazilian winger Malcom.
Despite Dembele being deemed by many as a huge talent for the future, the Frenchman struggled for both form and fitness in his first season in Barcelona following his £135m move from Borussia Dortmund in 2017. He scored three goals and provided seven assists in 17 La Liga games as La Blaugrana secured a league and cup double.
Ramsey meanwhile featured 32 times for Arsenal in 2017/18, scoring 11 goals and providing 12 assists in all competitions in what was a largely disappointing season for the Gunners, which saw them finish outside the Champions League places for the second straight campaign.
The two sides have been busy throughout the summer so far as they prepare for the season ahead, although Barcelona look to have pipped the Premier League outfit to long-term target Steven N’Zonzi after Arsenal refused to pay the price set by Sevilla for the holding midfielder.