SpringOwl, Cove Street say they have made specific suggestions regarding board composition.
Under pressure from Jana Partners, Houston company sells Australian, Canadian assets.
The sale of its chemicals and drilling fluids businesses will help Weatherford pay down more debt.
Oil and gas explorer is focusing its efforts on its more promising shale plays.
Having amended its debt covenants, the iron ore and coal producer said it could close its Bloom Lake development.
Merger would create the second largest energy services provider in the world.
Combination would challenge Schlumberger's dominance in energy services, but obstacles loom.
Goldman is advising Baker Hughes while Credit Suisse is assisting Halliburton on a possible merger.
Deal implies a five times return for Nuevo backer Encap Flatrock Midstream.
The deal moves the gas company closer to a pure play general partner holding company.