The Prisoners actor is currently in talks about the lead role, which rapper Eminem was previously attached to, reported The Wrap.
Jake would play a left-handed fighter who wins a title but then suffers a tragedy. He then has to rebuild his life in order to win the respect of his daughter.
Southpaw will be directed by Antoine Fuqua and production is due to start next year.
Jake, 32, can soon be seen in erotic thriller Enemy and crime film Nightcrawler.
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