The novel, a work of historical fiction, is set in colonial Kenya in the 1920s.
It centres on the life story of Markham, who became the first woman to fly solo across the Atlantic from east to west.
Raised in Kenya, Markham cultivated a love for adventure beginning at a young age, but when it came to love, she found herself in one disastrous relationship after another.
She eventually became involved in a love triangle with safari hunter Denys Finch Hatton and Karen Blixen, and, through her relationship with Hatton, discovered her love for flying.
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McClain previously wrote the hit 2011 novel "The Paris Wife," a fictionalised account of Ernest Hemingway's marriage to Hadley Richardson.
Lauren Sanchez is producing with Imperative Entertainment partners Dan Friedkin and Bradley Thomas, said The Hollywood Reporter.
Tim Kring is executive producing and vp content Jillian Apfelbaum overseeing for the company.
"I've known about Beryl Markham since I was a young girl," saud Sanchez, who is a pilot as well.
"She's that feminine icon that no one knows about. We want her story to be told."
"She was a pioneer for women. Everyone says Hollywood is looking for female-driven roles and stories - this is one of them.