Talks are at an early stage and could collapse or result in another structure for a Dow Jones bid, both papers reported.
GE owns the CNBC business television channel, which operates CNBC.com, and will face competition from News Corp., which is launching a business news channel of its own.
GE Chief Executive Jeffrey Immelt has taken a serious interest in the possibility, according to The New York Times.
Executives from NBC and CNBC, who were set to attend a conference in London this week, stayed behind in part because of the talks with Pearson, the Times said.
Under a scenario that has been discussed, CNBC, the FT and Dow Jones would be combined in a privately held joint venture, the Journal reported. The venture would be owned in equal parts by GE and Pearson, with the Bancroft family holding a minority stake in the new company, the Journal said.
GE and Pearson would each take a 40% or 45% ownership in the new entity, with the Bancroft family members holding 10 percent to 20 percent of the new company, which would remain private, the Journal reported.
The paper said this structure would allow some of the family members to sell their stakes while letting others roll their Dow Jones stock into the new company, avoiding any big tax bill.
The Journal reported that one family member said the Bancrofts had agreed they would give serious consideration to an offer that was lower than the $60 per share on offer from News Corp if they felt the buyer could better protect The Wall Street Journal's integrity.
A Bancroft family spokesman and a General Electric spokesman declined to comment. Pearson officials were not immediately available. Multiple Bancroft family members did not return telephone calls seeking comment, or they declined to comment.
Dow Jones also owns the Marketwatch.com business news Web site, the Factiva electronic news archive and Dow Jones Newswires, which compete with Reuters Group in providing business news.
Pearson has also sounded out Barry Diller's IAC/InterActiveCorp and privately held newspaper and magazine publisher Hearst Corp. as partners, the Financial Times reported. An IAC spokeswoman declined to comment.