Mendes, 42, who began dating the Canadian actor in 2011, gave birth to Amada on April 29 in Santa Monica, near Los Angeles, according to the entertainment news site.
Representatives for the American actress and Canadian star, 35, did not immediately confirm the report.
The stars already have a daughter Esmeralda, born in 2014.
For both pregnancies, Mendes, a Cuban-American born in Miami but raised in California, chose to rarely, if ever, appear in public, or appeared artfully wrapped in scarves and shawls.
Actor-director Gosling met Mendes on set while filming The Place Beyond the Pines (2012), in which they played a couple with a baby. Gosling, a frequent candidate on the world’s sexiest men list, is known for his roles in Drive and Crazy, Stupid, Love.
The actor — whose previous partners have included Sandra Bullock — was shortlisted for an Academy Award for 2006’s Half Nelson.
Gosling served up his hugely-anticipated directorial debut Lost River at the Cannes Film Festival in 2014, which had some critics screaming in pain and others singing his praise.
Last year he played an arrogant banker in The Big Short, and his police comedy The Nice Guys comes out this month.