The combined entity will be controlled by GE (ge) and would have publicly traded shares, the Journal reported, citing people familiar with the matter.
The deal is to be announced on Monday, the Journal said.
GE said in a statement last week that it was in talks with the oilfield services provider on potential partnerships but none of those options included an outright purchase.
A partnership with Baker Hughes could help GE to transform its oil and gas division and emerge a larger player in the sector to better compete with oilfield services leader Schlumberger.
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Also, this partnership could give Baker Hughes a chance to redefine itself following the failed merger.