The Gunners are looking at no European football next season after being knocked out of the Europa League and have now regressed from regular involvement in the Champions League to no involvement in continental competition.
Mikel Arteta is keen to add to his squad and looks to be eyeing introducing further goal threats into the team, with an eye on French hitman Dembele.
Dembele is currently on loan in Spain at Atletico Madrid from Lyon, but the club may not trigger their option to sign him on a permanent basis.
It is suggested that Dembele could cost Arsenal a fee in the region of £25m.
It remains to be seen if Dembele will be attracted to the idea of a switch to the Emirates Stadium with no European football on the agenda.
He has clocked just four appearances in La Liga for Atletico Madrid since joining the club in the January transfer window and is yet to find the back of the net.
Dembele is no stranger to the hustle and bustle of British football due to his spell at Celtic, where he hit 51 goals in just 94 games, tempting Lyon to splash the cash to sign him.
