The files also include further references to Ratner.
Emails from 2010 show Epstein tried and struggled to contact Ratner, exchanging emails with his assistant about the correct email address and phone number.
In 2011, the assistant apparently emailed Ratner to say Epstein wanted to speak to him. There is no evidence that Ratner received the messages or responded.
In an email from 2012, Epstein wrote to a publicist, apparently from the Cannes Film Festival, that he was “sitting next to Brett Ratner”, adding: “Brett says hi and he loves you!”
In a 2018 iMessage, Epstein wrote to an unidentified recipient: “Hi , im jeffrey. Brett ratner thought we should meet.”
BBC News has contacted Mr Ratner’s representatives for further comment.
The director is also known for making films including 2006’s X Men: The Last Stand and 2014’s Hercules.
His film about the US First Lady was released on Friday, being panned by critics but beating box office predictions by earning $7m (£5.1m) in its opening weekend.
It is Ratner’s first project since he was accused of sexual misconduct at the height of the #MeToo movement in 2017. Ratner has denied the allegations.