Tuesday was the deadline for Smith to inform the Knicks.
Smith's plans come as no surprise to the Knicks. The team expected him to test free agency rather than agree to play for $2.9 million after his breakout 2012-13 season.
Smith, 27, earned the NBA's Sixth Man Award after averaging 18.1 points and 5.3 rebounds per game. He played an integral role in the Knicks' regular-season success but struggled mightily in the playoffs, making just 33 percent of his field goals.
Still, retaining Smith is the Knicks' top offseason priority, according to a league source. They can offer him a contract starting at approximately $5 million per season with standard raises over four years, using the Early Bird exception.
Another club with ample cap space can offer Smith more money annually, but Smith has said he values his relationship with head coach Mike Woodson. Playing for the Knicks also provides Smith, a native of Freehold, N.J., the chance to be near his family.
If another team offers Smith a chance to start, it might sway his decision. Smith, a nine-year veteran, expressed disappointment early last season when Woodson informed him he'd be coming off the bench.
The Knicks would also like to re-sign Chris Copeland and Pablo Prigioni. Both are expected to test free agency and command strong offers on the open market. The Knicks might have to use their mini midlevel exception of $3.1 million to retain the players.
Because of salary-cap restrictions, New York has only the mini mid-level exception and minimum contracts to offer free agents.
On Tuesday, the Knicks extended their qualifying offer to Copeland, his agent, John Spencer, confirmed with ESPNNewYork.com.
"Cope is grateful the Knicks made the offer," Spencer said. "It shows they appreciate the value he brought to the team during the season."
The offer is for one year guaranteed at $988,872, and Copeland has until July 23 to accept it. If he doesn't by then, the Knicks can withdraw the offer.
Several other teams are interested in Copeland, who averaged 8.7 points per game last season as a rookie.
Ian Begley is a frequent contributor to ESPNNewYork.com. Information from ESPNNewYork.com's Jared Zwerling and The Associated Press was used in this report.