The 25-year-old joined Arsenal from Saprissa in the summer of 2011, but he has only made 23 Premier League appearances for the London club over the last six years.
Lorient, Real Betis, Olympiacos, Villarreal and Sporting Lisbon have all had the Costa Rica international on loan in recent seasons, but he is now back at Arsenal as he bids to overcome a knee injury.
Campbell managed just three goals during a difficult loan spell at Sporting last term, although his agent Joaquim Batica claimed earlier this summer that the attacker’s experience of top-level European football makes him an attractive proposition.
According to The Guardian, Arsenal are keen for Campbell to leave on another loan spell this season, but the Costa Rican has made it clear that he is reluctant to depart.
Arsenal, who will continue their 2017-18 Premier League season with a trip to Liverpool on Sunday afternoon, currently have 28 senior players in their first-team squad, which is three more than the Premier League limit.