The report claims that Trabzonspor have been keeping tabs on the Costa Rica international and will make an enquiry.
Campbell has been closely linked with a move to Turkey over the summer transfer window.
The 23-year-old forward has also been on the radar of Süper Lig champions Galatasaray and runners-up Fenerbahçe.
Campbell has been transfer listed by Arsenal after spending the last few seasons out on loan according to the Daily Mail.
The Costa Rican international was expected to feature for Arsenal last season after Gunners boss Arsene Wenger insisted that the Campbell remained at the club but he struggled for playing time and ended up being loaned out to La Liga outfit Real Sociedad over the winter transfer window.
Trabzonspor finished last season in fifth place and are currently competing in the Europa League play-off stages.