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.
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