The entertainment trade publication said SoftBank had offered $32 per share for DreamWorks, a substantial premium to the stock's Friday closing price of $22.36.
Buying DreamWorks, which is headed by veteran Hollywood producer and film executive Jeffrey Katzenberg, would make SoftBank the second Japanese technology company to buy a Hollywood studio, following Sony Corp, which bought Columbia Pictures in 1989.
SoftBank has recently cashed in on a share of its investment in Chinese e-commerce giant Alibaba and dropped its pursuit of mobile carrier T-Mobile US in the face of opposition from anti-trust regulators in the United States.
Last week, SoftBank booked a $4.6 billion gain on the share listing of Alibaba Group in New York. SoftBank retains a 32 percent stake, making it Alibaba's biggest shareholder.
SoftBank has significant stakes in other large listed entities, including U.S. mobile carrier Sprint, through which it had pursued a deal for T-Mobile, internet portal Yahoo Japan and online games maker GungHo Online Entertainment.
A SoftBank spokesman said the company had no comment on the reported talks with DreamWorks. A representative of DreamWorks could not be immediately reached for comment.
Move into content
In July, SoftBank hired former Google executive Nikesh Arora to run a newly created unit called SoftBank Internet and Media, reporting directly to Son, in a move that stoked speculation the telecommunications company could be considering a move to acquire content production assets.
SoftBank held the equivalent of more than $17 billion in cash and equivalents as of the end of June, its most recent reported quarter.
DreamWorks, based in Glendale, California, has seen its share price has drop 37 percent this year after two consecutive quarterly losses, a string of weak-performing releases such as "Mr. Peabody & Sherman" and investor concern about the production costs of its movies.
In July, DreamWorks said the U.S. Securities and Exchange Commision was investigating a writedown it took at the end of 2013 on the animated flop "Turbo".
Dreamworks Animation was spun off from DreamWorks Studios in 2004 as a separate listed company.
The earlier Dreamworks studio had been founded in 1994 by Steven Spielberg, David Geffen and Katzenberg, who moved with the spin-off and remains chief executive of the animation company, which also has the franchise hit "Kung Fu Panda" and owns the rights to Felix the Cat.
The move by SoftBank comes as Alibaba is also looking to expand its video content offered through a set-top box in China. In July, the company announced a partnership with Lions Gate Entertainment for its titles including "The Hunger Games".
Sony rebuffed a proposal from hedge fund Third Point to spin off its entertainment business last year in order to separate it from its loss-making electronics division.