"When we have the cap on, and its sealed and we know we've got a seal," the oil will be contained, Allen said, adding that a timeline provided by BP was being reviewed before the old cap is removed and the new one put in place.
"We're reviewing it right now," Allen said. "If there are no problems with it, we'll probably authorise them to move ahead later on this evening."
"It looks like it's achievable at this point if we remain on schedule.
"If we approve the timeline, we would start tomorrow to remove the current cap and to start the sequence of events."
BP has made several attempts to plug and contain the blownout well, which has been leaking oil into the Gulf since an oil rig exploded on April 20.
Since then millions of barrels of crude have polluted coastlines in all five US Gulf states and wreaked havoc on wildlife and ecosystems in the area.
The leak is expected to continue until mid-August, when two relief wells are to be completed. But if all the oil spilling into the sea can be contained, the disaster - already the worst in US history - should not get any worse.
The spill has become a major political issue in the US, complicating Washington's relationship with Britain and putting Obama under domestic pressure over his handling of the disaster.
His administration said on Friday that it would annouce a new moratorium on deep water oil drilling after US courts failed to extend an existing six month ban on drilling below 152.5 metres.
Opponents of the ban warn that it is too broad and could force multinational oil companies to withdraw from US waters, threatening jobs in an uncertain economic climate.
News that the worst of the spill might be over has given hope to investors who have watched BP's share price plummet as the crisis has developed.
The past two weeks have seen BP's shares gain 25 per cent in value as rumours that the energy giant is seeking new investors gave hope that the company would recover from the crisis.