The Sunday Mirror reports that Sunderland are interested in the defender and Nantes are reported to sell for around £5million.
The Senegal international has just one year left on his contract at the French club and is keen on a move to the Premier League.
“Papy has been doing wonders in France and he now he wants to try his luck in England,” said Djilobodji’s UK representative Chris Nathaniel to the Sunday Mirror.
“He is now looking for a new challenge and he feels the Premier League is the place for him to do that.”
The 26-year-old impressed for Nantes last season and the French side is desperate for the defender to sign a contract extension.