BP late on Saturday was waiting for the cement to set at the bottom of the ruptured Gulf of Mexico oil well before testing the strength of the seal.
If the seal passes the test, it will mark the final, formal step in closing down the well that caused the worst known ecological disaster in US ocean waters.
The pressure testing was set for 0400 GMT on Sunday, and could take one to two hours, the Wall Street Journal reported, quoting a person familiar with the situation.
A formal announcement of the results is not expected until later on Sunday.
A temporary cap halted the flow of oil in July. But BP, under supervision and requirements of the US government, has been completing the final seal of the well.
First, the so-called "top kill" forced mud and cement down the ruptured well pipe.
The second step, the so-called bottom kill, began earlier this week when BP's relief well intersected with the ruptured well four km below the ocean floor. Engineers finished Friday night pumping cement in at the bottom of the well.
The April 20 explosion on the Deepwater Horizon oil rig killed 11 workers and sent an estimated 4.9 million barrels into the Gulf waters and onto the fragile coastline.
The biggest marine oil spill in US history produced an environmental disaster area in Gulf waters and along the southern US coastline, and undermined the fish-dependent economy.
The final, deep sealing of the lower well will mark an end to what has been a financial and public relations nightmare for the British-based oil company. BP has already established a 20-billion-dollar trust fund to cover cleanup and economic impact in the Gulf region, but its eventual liability could be even higher.
The US government's National Oceanic and Atmospheric Administration insists that most of the oil has either been collected from the surface or dissipated through the use of underwater dispersants.
But scientists are questioning those claims, and say they have tracked 30-km-long underwater plumes of crude oil from the ruptured well. More recently, a professor at the Department of Marine Sciences at the University of Georgia has identified a centimetres-thick layer of oil infused into the ocean floor in the region near the disaster, and is awaiting tests of the "fingerprint" of the oil to confirm it came from Deepwater Horizon.
The researcher, Samantha Joye, says "the oil is not gone. It's in places where nobody has looked for it."