Al Jazeera's Nick Spicer, reporting from the town of Empire in Louisiana, said the next effort would likely start on Monday or Tuesday.
It would involve cutting out the well head and moving a multi-tonne devise called a blow out preventer, and then having a drill ship send down a long-pipe with a nozzle that would suck up the oil coming out, our correspondent explained.
BP has said that – if successful – the procedure will be able to get only a majority of the oil, not all of it, and the Obama administration said on Sunday that the amount of oil leaking from the ruptured well could increase as much as 20 per cent while efforts were made to cap it.
Experts also warned that the operation was risky because a bend in the damaged riser pipe was likely to be restricting the flow of oil.
"If they can't get that valve on, things will get much worse," Philip Johnson, an engineering professor at the University of Alabama, told the Associated Press news agency.
"It's a scary proposition."
BP engineers have said that a permanent solution to the leak, a relief well currently being drilled, will not be ready until August.
"We are going to have to wait a long time for a definitive solution to this crisis, which is really very bad news," our correspondent said.
"And it's not just the damage on shore. We are hearing more and more from scientists and oceanographers about what's going on under the sea, and will be for years if not decades to come," Spicer said.
"Scientists say there is a 30km long, 10km wide plume of oil about a kilometre under the water, potentially sucking up all the oxygen there, killing plankton ... creating a sort of dead zone in the Gulf of Mexico that will be spreading," our correspondent said.
Scientists from several universities have reported plumes of what appears to be oil suspended in clouds stretching for kilometres and reaching hundreds of metres beneath the Gulf's surface.
The findings - from the University of South Florida, the University of Georgia, Southern Mississippi University and other institutions – were based on initial observations of water samples taken in the Gulf over the last several weeks.
Activist Naomi Klein tells Al Jazeera patience running thin over response to oil spill
James Cowan, a marine scientist at Louisiana State University, who reported finding a plume last week of oil about 80km from the spill site that reached to depths of at least 122 metres, said "there's been enough evidence from enough different sources".
But Tony Hayward, BP's chief executive, disputed the scientists' claims, saying BP's sampling showed "no evidence" that oil was suspended in large masses beneath the surface.
"The oil is on the surface," Hayward said. "Oil has a specific gravity that's about half that of water. It wants to get to the surface because of the difference in specific gravity."
In the six weeks since an explosion hit BP's Deepwater Horizon drilling rig, killing 11 workers, the leaking well has spewed an estimated 68 million litres of oil into the Gulf of Mexico.
The spill is the worst in US history - exceeding even the Exxon Valdez disaster in 1989 off the Alaska coast.
BP says it has so far spent $940m to try to plug the leak and clean up the sea and soiled coast.
The top kill operation, which involved pumping mud into the well - most of which escaped out of the well's damaged riser pipe - was the latest of several failed attempts to plug the leaking well.
In the days immediately after the explosion BP engineers tried to use robot submarines to close valves on the massive blowout preventer atop the damaged well.
Two weeks later ice-like crystals clogged a 100-tonne containment box the company tried placing over the leak.
And earlier this week engineers removed a mile-long siphon tube from the broken riser pipe after managing to extract a disappointing 3.4 million litres of oil from the well.
|The leaking well has so far spewed some 68 million litres of oil into the Gulf of Mexico [AFP]
News that the top kill operation had failed was met with severe criticism from residents and the authorities on the Gulf coast.
"I'm devastated ... We are dying a slow death, every time that oil takes out a piece of the marsh, a piece of Louisiana is gone forever," Billy Nungesser, president of Louisiana's Plaquemines parish, one of the areas worst hit by the spill, said.
Mary Landrieu, a Louisiana Democratic senator, called on BP to immediately invest $1bn to protect marshes, wetlands and estuaries across the region.
She and David Vitter, a Louisiana Republican senator, urged BP and the federal government to immediately fund and support the plan to use dredging materials to create an offshore island barrier.
Barack Obama, the US president, who has called the leaking well a "manmade disaster", is trying to fend off criticism that his administration acted too slowly in its response to the spill.