Singleton, a 6-foot-8 forward, has played parts of five seasons in the NBA, recently with the Washington Wizards in 2011-2012.
He played the 2012-2013 season in China with the Xinjiang Flying Tigers, averaging 15.1 points and 11 rebounds in 21 games.
The Knicks will need to cut a player on their 15-man roster once their agreement with Singleton, 33, becomes official. The New York Daily News first reported the Knicks were close to a deal with Singleton on Wednesday.
Singleton should help offset injuries to the Knicks' front line. Tyson Chandler (bulging disk in neck) and Kenyon Martin (left ankle sprain) will miss at least the next two games because of their injuries.
Marcus Camby is doubtful for Thursday's game against Chicago because of plantar fascia in his left foot. So the Knicks need help on the front line as soon as possible.
It is unclear at this point who the Knicks will cut once they add Singleton.