The 38-year-old actress has given "The Notebook" star Gosling an ultimatum that if they don't seriously consider having kids soon they should split up, reported National Enquirer online.
"Eva's clock is ticking. She's been aching to start a family for years - and even seriously looked into adoption in the summer of 2010 but now she and Ryan are together and he's perfect husband and father material," a source said.
"He's loyal and not a skirt chaser. Eva has told Ryan that she wants a baby with him and that if he isn't prepared to do that they should split up," it added.
However, the 31-year-old actor isn't keen to have kids yet and it is causing problems for them with Mendes said to be torn about choosing between the man she loves and having kids.
"Ryan loves Eva but he isn't ready for a baby right now as he's concentrating on his career. Eva's considering her options. If Ryan doesn't change his mind, this could end up destroying their relationship," the source said.