Besides expecting a child, the couple could also be gearing up to get married very soon, reported Us! magazine.
"Eva is thrilled. She's been ready for motherhood for a while now, and to be sharing this experience with Ryan is a dream come true for her," a source said.
"Ryan grew up without a dad, so he always said when he had kids, he'd be there no matter what. This is it for him," it added.
The rumour seems to have been fuelled by an incident when the 'Place Beyond The Pines' star reportedly told officers Transportation Security Administration point for a routine pre-flight security check that she would not be able to pass through the body scanner "because she's pregnant"; a claim that was later denied by the actress.
Neither Mendes nor Gosling have commented publicly on the reports.