The couple, who have been linked romantically since September, were seen walking in the Pere-Lachaise cemetery in France over the weekend.
"They were holding hands and there was a lot of tenderness between them," a witness told People.
The Pere-Lachaise cemetery is the final resting place of a number of famous individuals, including Jim Morrison, Édith Piaf and Oscar Wilde.
Mendes is in town shooting Holly Motors opposite Kylie Minogue.
Gosling recently joked that he is in a "committed relationship" with acting, saying that he is dedicating most of his energy to his career.