Tony Hayward said the procedure would begin on Wednesday if considered safe.
Teams have been carrying out diagnostic tests to ensure the "top kill" method - in which mud is pumped into the well - is feasible and will not backfire.
Meanwhile, a congressional memo has revealed warning signs were present in the hours before the rig exploded.
According to the document, BP officials told congressional investigators on Tuesday that a decision to continue drilling after unusual pressure readings may have been a "fundamental mistake".
BP said the buildup of pressure was an "indicator of a very large abnormality" in the well, the memo by representatives Henry Waxman and Bart Stupak said.
Problems were also identified with equipment including the blowout preventer - meant to shut down the well in the case of emergency - and potential gas leakage in the hours prior to the 20 April explosion, the memo said.
BP is under intense pressure to succeed with its latest attempt to stem the leak, after previous measures failed.
"Later this morning I will review that with the team, and I will take a final decision as to whether or not we should proceed," Mr Hayward told the US network NBC's Today show.
"I have to say that it will be a day or two before we can have certainty that it's worked."
If the new procedure is used, heavy drilling fluids - such as mud - will be injected into the well about a mile (1.5km) underwater.
Engineers hope to follow this with cement, designed to seal the well.
The company has said they estimate a 60-70% chance of success.
Officials say the method has been used before in other areas of the world, but not at the depths required to stem the oil from the Deepwater rig, which sank after an explosion last month.
If the operation goes ahead, it can be watched via a live video stream of the site, which currently shows plumes of oil and gas escaping from the well.
A conservative estimate of the amount of oil escaping is about 5,000 barrels (210,000 gallons, 795,000 litres) a day while some scientists say it could be many times greater.
The US government has declared a "fishery disaster" in the seafood-producing states of Louisiana, Mississippi and Alabama.
A massive containment and clean-up operation is under way, as the oil reaches the beaches and vulnerable marshlands of a 150-mile stretch of coast.
Some workers involved in the operation are complaining of health problems after contact with oil and chemical dispersants, the Los Angeles Times reports.
The fishermen, who say they are suffering from nausea, dizziness and breathing problems, told the paper they were not issued with special equipment but were simply told by BP not to pick up oil waste.
Louisiana Congressman Charlie Melancon has urged the federal government to set up mobile clinics in rural area to treat those affected, the paper reports. BP has said conditions are being monitored.