The club sporting director Suleyman Hurma reportedly confirmed interest in the Senegal international.
“We have made our offer and will wait for a response now, it is normal for other clubs to also be interested,” Hurma was quoted as saying.
The Mirror report that Premier League outfit Sunderland are also interested in the 27-year-old defender.
Nantes want £5 million for the defender who has just a year remaining on his contract.
The report also claims that the experienced defender wants to play in the Premier League and that West Brom are also interested.
“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.
“He is now looking for a new challenge and he feels the Premier League is the place for him to do that.”
Trabzonspor have had a busy transfer window and have already signed Cavanda from Lazio, N’Doye from Hull City, Europa League winner M’Bia and Turkish international Okay Yokuşlu.
The Black Sea Storm beat Bursaspor 1-0 in their opening game of the season and take on Istanbul giants Beşiktaş next in the league.