The world's No. 3 oil and gas company, which has 20 oilfields in the gulf, hopes to reach an agreement within a month and restart several projects in July, the officials told The New York Times.
The Wall Street Journal said the British company was "waiting for final sign-off" and the Financial Times said the deal was already struck.
The U.S. Interior Department bureau that oversees gulf drilling told the Times, Journal and Washington Post no deal had been made with BP. BP declined to comment.
BP's petition comes ahead of the April 20 anniversary of the blowout on the Deepwater Horizon rig that BP had leased for an exploration well called Macondo Prospect.
The blowout killed 11 workers and injured 17 others, set the rig on fire and triggered the petroleum industry's largest marine oil spill, gushing for three months.
The leak was stopped July 15 after it released about 4.9 million barrels, or nearly 206 million gallons, of crude oil.
BP -- the world's fourth-largest company in revenue and the gulf's largest oil producer, pulling up 400,000 barrels a day -- seeks the drilling permissions to increase output in fields already producing oil, officials said. None of the drilling would be for new exploration, they said.
A condition of its permit would include BP's agreeing to give U.S. government overseers 24-hour access to its drilling operations, the officials said.
Gulf drilling was halted last summer because of the accident. The ban was lifted in October.
The bureau overseeing gulf exploration issued eight deep-water permits since Feb. 17, and BP holds a minority stake in one operated by Houston oil and natural gas exploration and production company Noble Energy Inc.
Royal Dutch Shell PLC last month received the first permit for a new deep-water well that hadn't been approved before the BP spill, letting Shell to drill an exploration well about 250 miles southeast of Houston. Shell also won approval Wednesday to drill off the coast of Louisiana on the condition it meets rigorous new safety standards.
Italian multinational energy firm ENI SpA won approval for a deep-water well Thursday.
Other companies allowed to continue drilling in the region include Exxon Mobil Corp., Chevron Corp. and Australian mining, oil and gas giant BHP Billiton Ltd.
U.S. officials have said any company that wants to resume drilling in the gulf would have to meet the new monitoring-safety requirements.
Environmentalists said that wasn't enough.
"It's hard to see how such monitoring will adequately mitigate the dangers of deep-water drilling," Greenpeace U.K. senior climate adviser Charlie Kronick told the Journal, adding he considered the decision to let BP back "premature."
Athan Manuel, a Sierra Club offshore-drilling expert, told the Post, "We don't think that BP has shown it's changed its corporate culture to earn the right to return to the Gulf of Mexico."