Shares of Juno soared 50 percent in premarket trading Wednesday on the report.
The news comes less than a week after the biotech giant announced it would buy Impact Biomedicines for $7 billion. Both Impact and Juno offer drugs that could boost Celgene in the market for blood-cancer treatment.
Celgene has been fighting to diversify its portfolio before its best-selling blood-cancer drug, Revlimid, loses patent protection, the Journal reported.
Jefferies analysts called the potential acquisition "smart," because "the buyout would enable Celgene to integrate Juno's entire cell therapy platform and bring it all in house."
Celgene has had an estimated $500 million stake in Juno since September 2017, according to a report from Jefferies.
Talks could lead to a deal in the coming weeks, sources familiar with the matter told The Wall Street Journal. Terms of a possible deal were not revealed.
Shares of Juno Therapeutics soared more than 34 percent on the news.
Representatives from Juno Therapeutics declined to comment to CNBC. Celgene did not respond to CNBC's requests for comment.