One of the most likely successors is BP Managing Director Bob Dudley, who is currently overseeing the British company's spill response. However, the government official did not know who will replace Hayward for sure.
Earlier on Sunday, BP officials tried to downplay media speculation about the CEO's departure. BP's board would have to approve a change in company leadership. An official announcement could come as early as Monday.
Since the explosion, Hayward has made several highly publicized gaffes. Among them: going to a yacht race while oil washed up on Gulf shores, and uttering the now-infamous: "I want my life back" line.
It's been more than three months since an offshore drilling rig operated by BP exploded off Louisiana on April 20, killing 11 workers and setting off the spill. A temporary plug has stopped oil from gushing for more than a week now, but before that the busted well had spewed anywhere from 94 million to 184 million gallons into the Gulf.
Work to plug BP's leaky well was getting back on the right track Sunday as crews worked quickly to take advantage of clear weather before another storm like Bonnie halted them yet again.
BP spokesperson Steve Rinehart said that relief tunnel drilling could resume in the next few days. Crews had to pull nearly a mile of steel pipe out of the water last week after evacuation orders were issued ahead of Tropical Storm Bonnie.
Although Bonnie lost strength on Louisiana's coast and skimmer ships returned to the spill area, the risk of another storm-related delay is high as peak hurricane season approaches.
"We're going to be playing a cat-and-mouse game for the remainder of the hurricane season," retired Coast Guard Admiral Thad Allen said.
- Completion now looks possible by mid-August, but Allen said he wouldn't hesitate to order another evacuation based on forecasts similar to the ones for Bonnie. In the past 10 years, an average of five named storms have hit the Gulf each hurricane season. This year, two have struck already - Bonnie and Hurricane Alex at the end of June, which delayed cleanup of BP's massive oil spill for a week even though it didn't get closer than 500 miles from the well. Hurricane season ends Nov. 30.
- Experts say that Bonnie may even have a positive effect. Churning waters could actually help dissipate oil in the water, spreading out the surface slick and breaking up tar balls.
The Associated Press contributed to this report.