The 28-year-old is apparently up for sale after his fall out with coach Eduardo Berizzo, and Jurgen Klopp is interested in signing him.
The Frenchman had an argument at half-time of Sevilla’s Champions League clash with Liverpool and the player ended up leaving the stadium.
He has since accused Berizzo of favouritism to other players and has skipped a training session too.
The French international has a £35m release clause in his contract and Liverpool are said to be weighing up a potential bid.
There is also a suggestion that a deal could be done which sees Daniel Sturridge make a move to Seville in a player-plus-cash transfer, but that seems unlikely at this stage.
Both N’Zonzi and his agent are in England looking for potential new clubs, with Sevilla’s permission, and time will tell if Liverpool join the likes of Arsenal and Everton in the race for his signature.