N’Zonzi has only 12 months remaining on his current deal but has publicly stated he is happy at Stoke after they finished ninth in the Premier League for a second successive season.
Scholes is therefore confident the Potters will be able to convince the 26-year-old to commit his long-term future to the club.
“If his football’s anything to go by, then it absolutely is reason to be positive we can get something done,” Scholes told The Sentinel.
“He had a magnificent season last year – and in fact he’s had three very good seasons with us, even if perhaps the last was his best.
“He’s playing with a smile on his face. He looks very happy and we would very much like to renew his contract.”
Scholes, meanwhile, has reiterated the club is in no rush to fill in a corner at the Britannia Stadium despite improved season ticket sales for next season.
“Filling in a second corner is on the agenda and we are always looking what ticket sales are like,” he said.
“We don’t want to build an extra section for it not to get used. We want to build one and fill it for every game.
“As soon as we get to the point when we think we can fill it for every game we will start.”