The 32-year-old actor is apparently planning on proposing to the actress, whom he met while filming "The Place Beyond The Pines", reported Daily Express.
"Eva was very clear to Ryan that she wants to be engaged before her 40th birthday, but Ryan was already on the case, and has been checking out rings - he's been planning on proposing for months," a source said.
The couple, who are extremely private about their relationship, are said to be looking to tie the knot at the end of the year.
But it's not just marriage that Mendes, 39, is thinking about. The "Hitchcock" star is also considering having children with Gosling.
"Eva has started to think seriously about kids with Ryan. She loves his family and gets along really well with his mum Donna - she even went with Ryan to Donna's college graduation last year.