"After the well is contained, BP may be a likely takeover candidate," Loretta Cross, a national managing partner at Grant Thorton's Corporate Advisory and Restructuring Services group, said during a conference call organized Tuesday by the American Bankruptcy Institute.

Cross, who specializes in energy company reorganizations, said a merger of equals or a takeover by a competitor would be a possible long-term solution for BP.

BP shares rose 1.6% to $27.47 during afternoon trading in the U.S. on Tuesday. The gains came as the Standard & Poor's 500 index slumped 2.9% on concern about a double-dip recession.

In a Tuesday note to investors, J.P. Morgan oil industry analyst Fred Lucas explored a merger and acquisition "fantasy" in which Exxon Mobil Corp. /quotes/comstock/13*!xom/quotes/nls/xom (XOM 57.32, +0.03, +0.05%) , run by Rex Tillerson, offers to buy BP /quotes/comstock/13*!bp/quotes/nls/bp (BP 27.76, +0.09, +0.33%) in 2011. He also mentioned Royal Dutch Shell /quotes/comstock/23s!e:rdsa (UK:RDSA 1,710, -59.00, -3.34%) /quotes/comstock/13*!rds.a/quotes/nls/rds.a (RDS.A 51.35, +0.14, +0.28%) as a possible bidder.

From April 20 through June 25, BP's market value plummeted almost $76 billion, relative to Exxon and Shell, Lucas noted.

"This substantially over-states the potential liabilities BP is likely to face, which we continue to estimate to be around $33 billion," Lucas wrote.

"In theory, either Exxon Mobil or RD Shell could consider a bid for BP" the analyst added. "They have similar business models and similar global asset structures. They also bear the lowest political risk to a potential combination with BP."

Russia's Gazprom /quotes/comstock/11i!ogzp.y (OGZPY 19.00, -0.76, -3.85%) may not be a realistic bidder because it has low-rated stock and more debt, limiting its financial firepower. PetroChina is financially stronger, but its acquisition of BP would probably hit political hurdles because the Chinese government is the controlling shareholder, Lucas explained.

Exxon's stock is rated higher than Shell's and the U.S. company has a stronger balance sheet, which would let it sweeten an offer to buy BP with more cash, Lucas said.

Exxon also has experience integrating a big acquisition, while Shell doesn't, the analyst added.

Lucas imagines a fictitious Exxon board meeting in February 2011 in which the topic of BP's future comes up. BP stock had continued to languish, despite the company's success in capping the leaking Macondo well.

Advisors were encouraging Tillerson "to make a pre-emptive offer using Exxon Mobil's more highly rated paper and so exploiting the stubborn rating differential that persisted," Lucas wrote.

The Exxon CEO was attracted by BP's high-quality assets, including its access to deep-water oil fields, the analyst continued.

"Rex prized asset control and he suffered no illusion, the deep water remained a vital source of reliable global oil supplies," Lucas wrote.

BP was also a "world-class" explorer and the company's trading operations could be down-sized. It also had low-cost liquefied natural gas business that would "complete Exxon's global jigsaw," the analyst wrote.

Anti-trust concerns focused on BP's downstream assets could be avoided by Exxon committing to spin off that business, Lucas said.

Speculation about a takeover of BP has already emerged. Earlier this month, Han Pin Hsi, an analyst with Standard Chartered Bank, said he'd seen "widespread media speculation" about a possible takeover of BP by PetroChina /quotes/comstock/13*!ptr/quotes/nls/ptr (PTR 110.51, -3.95, -3.45%) .

He said an offer would be supported by interested parties since it could transform PetroChina from a low-growth company to "China's global oil champion" and it would add to the oil giant's earnings.

"BP's long-term shareholders may now be more willing to sell due to the uncertainties besetting it: BP's Gulf of Mexico liability will not be known for some time and future dividends could also be cut," Hsi said in a note to clients.

"Furthermore, the weak market/oil price suggests that PetroChina would not have to pay a significant premium over the long-term value of the assets. All this would change next year if oil strengthens above $100, as we expect it to," he added.