French regional news outlet La Depeche du Midi claims the 26-year-old was arrested in Toulouse for allegedly making repeated death threats to his former partner.
A source told the newspaper: "He is suspected of having repeatedly threatened his partner, aged 29, whom he is separating from.
"Their divorce, which began months ago, is taking place in a climate of conflict."
The report adds that the complaint was filed last week, but police officers had to wait until he returned to Toulouse in order to arrest him.
It has been claimed that he is still in police custody.
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A Fulham spokesperson said in a statement: "We are aware of reports emanating from France this morning regarding one of our players, Issa Diop.
"We are currently liaising with the player's representatives to establish the facts."
Diop joined Fulham in August 2022 in a £15million move from West Ham.
He spent four seasons at the London Stadium, making 121 total appearances for the club.
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The defender played 25 Premier League games for Fulham this season as they finished 10th.
The 26-year-old came through Toulouse's academy and went on to make 95 appearances for his hometown club.
He joined the Hammers in 2018 on a then-club record deal said to be worth around £22m.