The Wall Street Journal, citing unidentified people, said on its website Thursday that talks were moving quickly and could result in a deal soon. No possible price was reported. At the start of trading, Baker Hughes' stock market value was $22 billion.
A spokeswoman for Baker Hughes said the company would not comment on market rumors or speculation. Halliburton representatives did not immediately respond to phone and email requests for comment. Both companies are based in Houston.
The report of deal talks comes during a drop in oil prices that has hurt both companies' stock price.
Baker Hughes shares closed up 15 percent at $58.75. Halliburton gained 56 cents to $53.79.