Billy King's reign in Philadelphia appears to be over.
Stefanski is expected to sign a multiyear contract, and his introduction will come at a Tuesday news conference, according to the newspaper.
Stefanski will replace King, who has been with the franchise since 1997 and has been serving in the dual roles of president and general manager since May 2003.
The Sixers fell to 5-12 after Monday night's 88-79 home loss to the Atlanta Hawks, leaving them with their 10th loss in 13 games and a 3-6 record at home.
A source told the newspaper that the Sixers contacted the Nets about a week ago, securing permission to speak with Stefanski, who has roots in Philadelphia.
Stefanski played for the University of Pennsylvania and was head coach at his alma mater, Monsignor Bonner High.
Stefanski is in his ninth season with New Jersey. He was promoted to GM in the summer of 2004.