The Frenchman, formerly of Arsenal, moved to the Estadio Ramon on loan in the summer transfer window after talks with new Manchester City boss Pep Guardiola.
The 29-year-old has scored twice in six appearances for the Spanish side this season and has played a key role in their impressive start to the 2016-17 campaign, which has left them in third position in La Liga.
Nasri has paid tribute to Sevilla boss Jorge Sampaoli and believes that he has been given a new lease of life in Seville.
"I have a relationship built on trust with the coach, and that is invaluable. It's thanks to him and to his assistant that I am here with Sevilla," Nasri told RMC Sport.
"I made the decision to come to Sevilla because I know that this club has been good for so many players – it has rekindled their careers and got them going again, I feel that happening to me."
Nasri only made one Premier League appearance for Man City last season due to injury.