The preventer, which is the subject of a subpoena, could be removed by Tuesday, The (New Orleans0 Times-Picayune reported Saturday.
It will be brought ashore and replaced by a second preventer that is better able to handle the pressure expected to build up when the well is filled with mud and cement in September as part of the final capping phases.
BP gave up on trying to fish three pieces of pipe from the preventer, two of them less than 14 feet long, but one of them 3,500 feet long. Instead, as it lifts the preventer, the shorter pieces will remain in place, while the longer pipe is cut away, the newspaper said.
A capping stack, which will also be removed, will be placed on the sea floor near the well in case it is needed in the event of a "low-probability, high-impact outcome" of capping the well, Allen said, referring to a possible second oil leak.