"I like that. I appreciate that. I think that sounds like a good thing. It's hard for me to be objective but I hope that's true." Paul Dano is speaking from an editing suite in New York where he's snipping and splicing at his directorial debut, Wildlife, set to hit cinemas this autumn. If his response to questioning is anything to go by, the film will emerge from a supremely considered edit indeed.

I'd asked if Dano agreed with the assertion that his presence on screen was often especially physical, in light of roles such as the convulsive preacher Eli Sunday in Paul Thomas Anderson's oil fable There Will be Blood (2007), or the quivering pariah Alex Jones in Denis Villeneuve's 2013 thriller Prisoners. As with most answers he gives, his response is measured, as if double-checking his opinion on the matter is what he actually thinks. Asked to explain the plot of his new film, Okja, however, certainty comes easily. "It's the story of a girl and her giant pig. I said, 'Oh my god, a girl and her giant pig sounds fucking great, I'm in.'"

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Gucci: Navy/red pindot wool suit, £1,710; pink silk-crêpe shirt, £530; black leather soft-back horsebit loafers, £505, all by Gucci

The film, dreamed up by South Korean director Bong Joon Ho (The Host, Snowpiercer), tells the story of Mija, a young girl whose best friend, Okja — the giant pig in question — is stolen by a boorish multinational company, headed up by Tilda Swinton, that takes the beast to New York for dubious commercial gain. A quest ensues, and Mija leaves her home in the South Korean mountains to reclaim her beloved friend.

"The seed of the film," Dano explains, "I found really exciting. It's a very ordinary person in a super-extraordinary situation. It sounded Spielbergian in some ways. It sounded big. With a big heart and a big mind."

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Maison Margiela: Black/white embroidered cotton tuxedo jacket, £POA; white cotton-jersey T-shirt, £110, both by Maison Margiela

Dano was also attracted to Okja because of his admiration for Joon Ho. "He's definitely a master," says Dano. "His tone, the stories he's interested in; his films only he could make." That sense of singularity is a common theme in the actor's impressive CV. In addition to Thomas Anderson and Villeneuve, he's worked under the direction of Richard Linklater, Ang Lee, Spike Jonze and Steve McQueen. His co-star list includes Michael Caine, Robert De Niro and Daniel Day-Lewis.

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Margaret Howell: Charcoal/black dogtooth soft wool-linen blazer, £735; grey cotton sleeveless sweater, £395; white/black striped cotton short-sleeved shirt, £275; black linen tapered trousers, £385; white leather derby shoes, £475, all by Margaret Howell

"The people I've worked with, there's a certain feeling on set, a certain temperature," says Dano. "Great film-makers, great actors, that's what they bring. It really creates a place, or a world, whatever you call it, to step into."

No doubt Dano looked to create that same temperature on his own set, and the hope is that Wildlife, starring Jake Gyllenhaal and Carey Mulligan, will be the first of many. How has he found moving behind the camera? "It's so scary and challenging, and also so big and delicious; you oscillate between those daily. But I think I do that with acting as well: you're lit up one moment, you're in despair the next."

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Ami: Navy wool-cotton jacket, £480; burgundy/navy/white cotton sweater, £255, both by Ami

One would imagine oscillation was never more apparent than in his Golden Globe-nominated portrayal of the young Brian Wilson, the troubled leader of The Beach Boys, in Love & Mercy (2014). Dano is also a musician (his band Mook released an eponymous album in 2011), so getting into the mindset of one of the 20th century's great songwriters was especially resonant. "Music is so fun and quick into the bloodstream," he says, "so to spend six months listening to studio sessions and learning how to play the piano and singing those songs, it brought a lot of joy to my life, even though the character struggled so greatly. It was really hard but it was also really fun."

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Sandro: Beige cotton trench coat, £530; white cotton-linen short-sleeved shirt, £165; indigo denim jeans, £155; brown leather buckled derby shoes, £370, all by Sandro

Beyond music, Dano is a sports lover; playing and watching. He is a Knicks fan, watches hockey, was glad to see Sergio Garcia win this year's Masters golf tournament, and is "definitely on the Roger Federer tennis train". Fashion is less of a passion (despite how good he looks in our shoot). "I don't want to put too much effort into how I look in the morning," he says, "but there can be pleasure in fashion. I see the way people dress themselves and feel good, and it's interesting." A pause for more signature Dano rumination… "But I think I might like fashion as a spectator."

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Pringle of Scotland: Black jersey-twill blazer, £695; black/white striped poplin blazer, £750; white cotton T-shirt, £145, all by Pringle of Scotland
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Burberry: Blue striped denim work jacket, £595; white cotton-jersey T-shirt, £85; blue striped denim work trousers, £395, all by Burberry
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Joseph: Brown cotton jacket, £445; grey Argyle knit polo sweater, £195; brown cotton trousers, £225, all by Joseph

— Interview by Charlie Teasdale

— Photographs by Neil Gavin

— Fashion by Catherine Hayward

— Okja is out via Netflix on 28 June