The deal talk between the two Houston-based companies comes during a drop in oil prices that has hurt both companies' stock price.
Combined, Halliburton and Baker Hughes would be slightly larger by revenue than Schlumberger (SLB) , and hold an even larger advantage in North America, where hydraulic fracturing, or fracking, is a big business for the oilfield companies.
A combination could give Halliburton and Baker Hughes more power to charge energy companies higher prices, particularly in North America.
Baker Hughes shares closed up 15% at $58.75. They added another 3% in extended trading after the company confirmed the deal talks. Halliburton gained 56 cents, or about 1%, to close at $53.79 and tacked on another 68 cents in after-hours trading.