The date took place shortly after Page and DiCaprio starred together in the 2010 Christopher Nolan thriller Inception.
In his candid new memoir Pageboy, Page opened up about his dating history, claiming that his mother had been unsupportive of his relationships with women. In 2014, Page came out as gay; six years later, he came out as transgender.
“While filming Inception, a friend of Leonardo DiCaprio’s visited and we had a lovely connection,” Page wrote in the memoir.
The friend of DiCaprio’s is identified in the book only as “Peter”.
“Peter was warm to everyone, eyes beaming with care. When I saw Leo next, I told him I liked his friend, to which he responded that his friend liked me, too,” Page recalled.
“For our first date we went to [US-based theme park] Universal Studios with Leo and his mother. Peter and I sat close on the rides, our thighs just touching.”
Page claimed that his own mother had been “over the moon” with her budding romance. However, it came to an end after “a month, maybe two”.
Elsewhere in the memoir, Page revealed he had once had a relationship with House of Cards star Kate Mara, shortly after coming out publicly as a lesbian.
He wrote about growing sick on the set of Inception as a result of the stress of feeling “out of place” amid a cast “full of [cisgender] men”.
Page also recounted his experience of a terrifying transphobic attack that took place in Los Angeles last year, and revealed details of a romantic fling with Olivia Thirlby, his co-star on the acclaimed 2007 comedy Juno.
Pageboy is out now.