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Paparazzi photos printed in the New York Post on Monday showed the actors kissing while enjoying a meal with members of Lopez's family at Malibu's posh Nobu sushi restaurant west of Los Angeles on Sunday.
Representatives for Lopez (51) declined to comment on Monday, while Affleck's publicists did not return a request for comment.
Lopez and Argo director Affleck (48), dubbed "Bennifer," became the most talked about couple in the celebrity world in the early 2000s in a romance marked by his-and-her luxury cars and a large 6.1-carat pink diamond engagement ring.
They abruptly called off their wedding in 2003 and split up a few months later.
The pair have been pictured together several times in Los Angels and Miami in recent weeks, after Lopez and her former baseball player fiance Alex Rodriguez called off their engagement in mid-April after four years together.
Monday's photos were the first in which Lopez and Affleck were seen kissing this time around.
Celebrity outlet E! News quoted an unidentified source last week as saying Lopez was planning to move from Miami to Los Angeles to spend more time with Affleck and was looking for schools for her 13-year-old twins Max and Emme.
Max and Emme, along with the singer's sister Lydia, were also photographed walking into the restaurant in Malibu on Sunday.
Lopez married Latin singer Marc Anthony, her third husband, just five months after her 2004 split with Affleck.
Affleck went on to marry, and later was divorced from, actress Jennifer Garner.