The 28-year-old striker has fallen out-of-favour at the Juventus Stadium this season, and has made just 16 Serie 'A' appearances for the defending champions.
Arsenal were thought to be monitoring his availability, but the Italy international has pledged to fight for his future at Juventus.
Speaking to Italian news site TuttoSport, Matri said: "It's clear that I want to play in every game, but I've always felt like the club have backed me, that they have always been close to me. That's a nice thing for players who are not used all of the time.
"When I've been called into action I've been ready and the side hasn't missed who I have replaced. If I am made to feel like an important player then I would prefer to stay at Juventus, rather than join another club who could perhaps offer me more playing time."
Matri has six league goals and two Champions League strikes this term despite his limited playing time, and plenty of suitors would be interested in signing the forward should he become available.
But the Italian conceded he could reassess his options at the end of the season - if his playing time continues to slide in Turin.
"If the time comes where you start to lose faith then it is better to change clubs," Matri continued. "Yet that moment hasn't arrived yet. If it does then it will be me who asks to leave."
Matri joined Juventus initially on a loan deal from Cagliari and nine goals in 16 league appearances convinced the Old Lady to bring him on a permanent basis.
He signed in 2011, but has since struggled to hold down a first-team place, with Sebastian Giovinco, Fabio Quagliarella and Mirko Vucinic all preferred to Matri this season.