Wallace first worked out for the Knicks last Saturday and had been contemplating a return in recent days.
The 15-year veteran retired after the 2009-10 season, which he spent with the Boston Celtics.
Wallace has not yet signed a deal, according to a team source. But the Knicks expect him at training camp, barring something unforeseen between now and the first day of camp Tuesday.
Wallace took a physical with the team late last week and has been working out at the Knicks' facility for most of the last week.
The New York Post reported on Saturday that Wallace would join the team on Monday.
The 38-year-old Wallace has ties to the Knicks. He played under Mike Woodson in Detroit. Woodson was an assistant under Larry Brown when the Pistons won the 2004 NBA title and was considered one of the main architects of Detroit's stingy defense.
Bill Strickland, Wallace's longtime agent, would not comment on his client's decision, out of respect for Wallace's privacy. But Strickland called Wallace's relationship with Woodson a "positive" one on Friday.
Wallace, a 15-year veteran, spent the bulk of his career with Portland and Detroit. He retired after a run to the 2010 NBA Finals with the Celtics, leaving nearly $12 million in guaranteed money on the table. According to reports, Wallace was out of shape early in his season with Boston, but seemed to get into form as the year continued.
In New York, Wallace likely will back up power forward Amare Stoudemire. Widely known for his penchant for technical fouls, Wallace is also a strong post defender and can knock down the perimeter shot.
The Knicks have Jason Kidd, 39, Marcus Camby, 38, and Kurt Thomas, 39, on the roster. Bringing in Wallace only would enforce the notion that this is a win-now team and that Woodson is more comfortable coaching veterans than younger players.
With Wallace in tow, the Knicks will enter camp with 20 players under contract, the maximum allowed per league rules.
If Wallace's deal is guaranteed, they would have one roster spot open for another free agent or one of the six players they've signed to deals that are not fully guaranteed. (NBA rosters can have a maximum of 15 players on opening night).
While waiting on Wallace's decision, the Knicks had reached out to representatives for free agent swingman Josh Howard, according to a league source.
If Wallace signs a guaranteed deal with the Knicks, it likely will be for the veteran's minimum of $1.7 million.
Ian Begley is a regular contributor to ESPNNewYork.com.