The 26-year-old was ruled out of the season after undergoing shoulder surgery and was placed on injured reserve. He has been replaced in the lineup by rookie Geno Smith, who has been inconsistent in the campaign.
"I don't want to go anywhere else," Sanchez told the Newark Star-Ledger.
"I plan on being here. That's all I'm thinking about, is coming back next year, leading this team and playing well. We'll see what happens."
Sanchez has thrown 68 touchdowns in his career, throwing for 12,092 yards since being drafted in the first round of the 2009 Draft.