The 19-year-old announced through a video on YouTube on Monday that he is dating a man, a revelation which received widespread support from celebrities and fans alike.
The Sun said today Daley was in a relationship with Dustin Lance Black, 39, who won an Oscar for the 2008 film Milk, which is based on the life of Harvey Milk, the first openly gay man elected to public office in California.
The pair are said to have been introduced by friends at the Soho Hotel in London earlier this year and Daley has reportedly made a number of trips to California, where Black lives.
Black, who is also a producer and director, is a founding board member of the American Foundation for Equal Rights and is regarded as one of the most powerful LGBT (lesbian, gay, bisexual, and transgender) people in America.
Since winning the Academy Award in 2009 he has dedicated much of his time to the political fight for LGBT equality, recently campaigning against ant-gay laws in Russia.
He also wrote the screenplay for the Leonardo DiCaprio film J Edgar, and is working on the film Earthquake for director JJ Abrams.
Daley was back at training yesterday with his fellow divers at the Life Centre pool in Plymouth, The Sun said.
As he left he said: "Everyone has been so supportive of me, it's absolutely fantastic. Everything I've wanted to say has been in the video, but thanks everyone for the support."
His diving colleague and friend Tonia Couch, 24, said she had known Daley was in a gay relationship for some time.
She said: "I'm so so proud of him. I've known for a while so it's great he's done it."
In his YouTube admission, Daley said he "couldn't be happier" after revealing his relationship.
"I've never really had a serious relationship to talk about," he said. "Now I kind of feel ready to talk about my relationships.
"Come spring this year, my life changed massively when I met someone and it made me feel so happy, so safe and everything just feels great. And that someone is a guy."
Daley said the relationship "felt right" and instantly changed his world.
"Of course I still fancy girls. But I mean, right now I'm dating a guy and I couldn't be happier. It makes me feel safe and just really does feel right," he said.
On Tuesday, Daley took to Twitter to show his appreciation for the support he received following the announcement, saying: "I'd just like to say again a massive thanks for all the support yesterday...it truly was overwhelming xx"