Many directors argued, citing a report from financial advisers, that Sony could compete better by maintaining close links between the entertainment and electronics divisions, the Japanese business daily said.
Sony's board has yet to finalize its position but is leaning toward a rejection, it said.
Daniel Loeb proposed in May that the company sell off as much as a fifth of the group's money-making entertainment arm - movies, TV and music - to free up cash to revive the electronics business.
Sony's U.S.-listed shares were down 2 percent at $21.19 in afternoon trading on the New York Stock Exchange.
Sony declined comment on the Nikkei report, saying in an email to Reuters that its board and management continued to review the Third Point proposal. Third Point did not respond to a request for comment.
Last year Sony was Hollywood's strongest studio with 16.6 percent of the U.S. box office. But it released two bombs this summer and its market share has dwindled to 8 percent so far this year.
Will Smith's film, "After Earth", and "White House Down", starring Jamie Foxx and Channing Tatum, both opened well below industry expectations for such big budget productions.
It had enjoyed a boomer year least year, boosted by blockbusters "The Amazing Spider-Man" and the James Bond film, "Skyfall".
In a note to investors on Monday, Loeb ratcheted up the pressure, saying Sony's entertainment business was poorly managed with a bloated corporate structure and marketing budgets that did not seem to be in line with the return on capital invested.
Loeb said Sony Chief Executive Kazuo Hirai deserved praise for the green shoots visible in electronics but faulted him for saying the entertainment business was doing just fine.
Sony will consider disclosing more financial information about the entertainment division, which Third Point says lacks transparency, the Nikkei said.
Hirai pleaded in June for patience from shareholders as the Sony board considered the proposal.
Sony's shares have risen around 14 percent since Third Point's push for an IPO of the entertainment division was made public in mid-May.
© Thomson Reuters 2013