The 27-year-old has been one of the key players in a remarkable season for his club, who are currently on course for a surprise fourth-place finish that would clinch Champions League football for next season.
Marca believe that the Gunners have expressed interest in the Togo international and are intent on signing him despite not yet making a bid.
Djene was already attracting the attention of other clubs last summer but was convinced to stay on for another season.
He could now be set for an exit, but any potential buyers are likely to have to meet his release clause of €35 million (around £30 million).
The former Sint-Truiden defender has made 32 La Liga appearances for his side this season.
Read more...
FEATURE How Johan Cruyff reinvented modern football at Barcelona
QUIZ! Can you name the 55 Europa League semi-finalists since 2000?
'Obviously Messi is the best player in history and being compared to him means that you're doing things right, but I try to be myself': Barcelona star responds to comparisons with Argentine legend
'Darwin Nunez would be gold for Arsenal': Liverpool legend claims Gunners should have signed Uruguayan striker in January
