City have reluctantly allowed the 26-year-old to discuss the switch after the Primera Division side tabled a bid believed to be around £7million.
N'Zonzi has a year left on his current contract at the Britannia Stadium but Stoke's attempts to persuade him to stay appear to have fallen on deaf ears.
Manager Mark Hughes told Sky Sports News : "We have allowed Steven permission to speak to Sevilla
"We worked really hard to persuade him his future lay here but it didn't seem to be enough for him
"He's been granted permission so we'll see where it takes him."
Frenchman N'Zonzi arrived in England when Blackburn signed him from Amiens in 2009
He moved on to Stoke for £3million in 2012 and has made 120 appearances for the club, scoring seven goals
Stoke have named N'Zonzi and goalkeeper Asmir Begovic, who has been linked with a move to Chelsea, in their squad for a pre-season tournament in Singapore next week
However, the club say the squad is subject to change
Source : PA
Source: PA