A deal could see SoftBank Corp, which controls internet firm Z Holdings, and Line's parent Naver Corp form a 50:50 venture that would control Z Holdings, which would in turn operate Line and Yahoo, the sources said.
The two parties were likely to reach a basic agreement by the end of the month, the sources said.
Naver was not immediately available for comment outside of business hours. SoftBank said nothing had been decided.
The talks were first reported by Kyodo news agency.
Line, which last year sold a majority stake in its mobile unit to SoftBank, has reported three consecutive quarters of operating losses as the company tries to jump start growth.
Z Holdings, formerly known as Yahoo Japan, made a move in September to take control of fashion e-tailer Zozo Inc in a $3.7 billion deal, as it bulks up against rivals like Amazon.com.
Dealmaking by SoftBank Corp, controlled by tech conglomerate SoftBank Group Corp, comes despite weak performance of its technology bets of its parent, which recorded an $8.9 billion operating loss in the second quarter.
The group's first quarterly loss in 14 years followed a collapse in the value of its investment in office-sharing firm WeWork as investors have turned sceptical about the path to profitability at cash burning startups.
(Additional reporting by Munsif Vengattil in Bengaluru; Editing by Maju Samuel and Edmund Blair)
By Noriyuki Hirata and Sam Nussey