The company had been approached by several investors, said chief executive Philippe Dauman, and would be holding talks with some investors.
Viacom is under pressure to revive its fortunes after a run of poor results.
Earlier this month it posted a 6% year-on-year fall in quarterly revenues to $3.2bn (Â£2.2bn).
Paramount Pictures has also struggled, with revenue falling 15% and an operating loss of $146m.
The studio, which Viacom says is rebuilding after some high-profile failures, is worth $4bn, Sanford Bernstein analyst Todd Juenger estimated this week.
The company did not say what percentage of Paramount it might sell.
China's Alibaba and Amazon have been suggested as potential partners by Viacom shareholders.
The Paramount sale announcement saw shares in Viacom down more than 1% in after-hours trade in the US.
The firm, which owns the cable channels Nickelodeon and Comedy Central, has seen its shares lose more than 40% over the past 12 months.
Its cable channels have struggled to maintain audiences amid a trend for younger viewers to watch entertainment on mobile devices and computers.
The chairman, 92-year-old Sumner Redstone, was recently replaced by Mr Dauman.
However, Mr Redstone, whose ability to lead the firm had been in doubt in recent months, controls about 80% of Viacom voting shares.
The Hollywood studio DreamWorks, best known for the Kung Fu Panda and Shrek movies, has posted better-than-expected quarterly profit and revenue, sending its shares up more than 9% in after-hours trading in New York.
Revenue for the three months to December rose by 36.3% to $319.3m, the firm said, while net profit came to $42m compared to a loss of $263.2m in the same period a year earlier.
The positive numbers were helped by DreamWorks' film The Penguins of Madagascar and the television release of its animation comedy Home.
Chief executive Jeffrey Katzenberg said DreamWorks had delivered "its best top-line result in 11 years and highest revenue growth in eight years".
Viacom is planning to sell a "significant" minority stake in its film and television studio Paramount Pictures.