Dow Jones reported the news, citing two people familiar with the situation.
Sun bought Captain D’s from Charlesbank Capital Partners for an undisclosed amount in May 2010, and has cut the number of restaurants in the chain from 539 to just over 520 in the intervening years.
The business operates across 25 states and in military bases around the world.
Sun is currently attempting to draw in commitments for its fifth major buyout fund, which held a $1bn first close towards its $3bn target in December 2012.
The firm had previously hoped to complete the entire fundraise by the end of last year, a feat which proved too optimistic in the post-financial crisis environment.
In March the firm exited its stake in the top frozen strawberry product maker in the US to fellow private equity firm Paine & Partners.
Sun bought into Sunrise Growers-Frozsun Foods in 2008 and said it improved growth and profitability through “cost saving initiatives, facility consolidations, key customer additions, new product introductions and business rationalisations.
Financial details were not disclosed, and a spokesman for Sun said it declined to give a sale price, exit multiple or net IRR for the investment.
Last month the firm announced it was seeking to combine five of its portfolio companies to create one of the world’s largest packaging companies.
Sun acquired Exopack in 2005, and is looking to combine the flexible plastic packaging company with its portfolio companies Britton, Kobusch, Paccar and Paragon.
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