Wallace had until midnight ET Wednesday to decide on his $9.5 million player option for 2012-13.
Wallace now becomes an unrestricted free agent. He had said he wasn't going to play on a one-year deal.
General manager Billy King said Wallace deserves a multiyear deal and wants to re-sign him.
Wallace, 29, averaged 15.2 points, 6.8 rebounds and 3.1 assists in 16 games after being traded to the Nets.
King dealt his team's first-round pick in the 2012 draft (No. 6) to the Portland Trail Blazers in a highly scrutinized move for Wallace.
Mike Mazzeo is a regular contributor for ESPNNewYork.com.