Obama has faced fierce criticism over his response to the spill, the worst environmental disaster in US history.
On Tuesday he is due to give a major speech focusing on the response to the spill so far and strategy in the coming months.
He will meet with BP executives on Wednesday at the White House to discuss damage claims and the next steps in stopping the leak.
'Billions of dollars'
Bill Burton, a White House spokesman, said the White House and BP were "working out the particulars," such as the amount of the compensation fund and how it will be administered.
The account would be controlled by an independent third-party entity, Burton said, and would run into "billions of dollars," although he would not give a specific amount.
"We're confident that this is a critical way in which we're going to be able to help individuals and businesses in the Gulf area become whole again," the spokesman said.
BP's board met on Monday in London to discuss deferring its second-quarter dividend and putting the money into escrow until the company's liabilities from the spill are known.
Sheila Williams, a BP spokeswoman, said the company was aware of the White House's demand for a compensation fund, but declined to comment further.
The US administration had said earlier that Obama was prepared to force BP, if necessary, to set up the fund.
Senior state level officials in Florida and Louisiana have said they want BP to put $7.5bn into the fund.
In Alabama, Mississippi and Texas, who have also been affected by the spill, officials have yet to announce how much they want from the company.
Some analysts have raised concerns that claims for compensation and clean-up could bankrupt the energy giant.
BP said on Saturday that it was "not in discussions with" and had "not engaged any bankruptcy experts".
Admiral Thad Allen, the coast guard official leading the government response to the disaster, has said BP must provide him with a "faster plan" to respond to the disaster.
At least a million barrels of oil have spewed into the Gulf of Mexico since the Deepwater Horizon rig exploded on April 20 and sank two days later.