A spokesman for Lopez also confirmed to Us Weekly and People magazines that she had ended the courtship, adding: "At this difficult time, we ask that you respect her privacy."
Affleck's publicist, Ken Sunshine, told the AP, "As usual, we never comment on the private lives of our clients."
The celebrity wedding would have been the third for Lopez, 34, and the first for Affleck, 31. The couple met in 2001 while filming the summer flop, Gigli. At the time, Lopez was married to dancer Cris Judd, her second husband. Lopez filed for divorce from Judd in July 2002, citing irreconcilable differences.
In November 2002, Lopez announced the news of her engagement to Affleck in an interview with Diane Sawyer on ABC's Primetime. Lopez described her feelings to Affleck as being "bigger and realer" and "totally different" from anything she had ever felt before.
The media has since been obsessed with the couple--dubbed "Bennifer"--following and analyzing their every move, including their recent trip to a Georgia courthouse where Affleck obtained a gun permit.
Lopez and Affleck appear in the upcoming dramatic comedy Jersey Girl, directed by Kevin Smith, hits theaters March 19. In the film, Lopez plays Affleck's wife, who dies within the film's first 15 minutes.