The untitled film will recount the Winehouse's life and career, said the Hollywood reporter.
Focus Features International, a division within the Universal Music will shop the high-profile project to foreign buyers at Cannes.
"This is an incredibly modern, emotional and relevant film that has the power to capture the zeitgeist and shine a light on the world we live in in a way that very few films can," said director Kapadia and Gay-Rees.
"Amy was a once-in-a-generation talent who captured everyone's attention; she wrote and sung from the heart, and everyone fell under her spell.
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Winehouse rose to fame with her second album, 'Back to Black' which sold more than 12 million copies worldwide since its release in 2006.
Winehouse died of alcohol poisoning in July, 2011.
"Asif and James have the remarkable ability to bring a moving and thought-provoking story to life, as evidenced by Senna. We look forward to seeing their vision of Amy Winehouse," Alison Thompson, Focus International co-president said.