NEW YORK (CNNMoney.com) -- BP's stock continued to run higher Monday, rising more than 6% in early trading, after reports that the company or some of its assets may be sold off.
In addition, the company indicated it is getting closer to containing the Gulf of Mexico spill.
In early Monday U.S. trading, BP shares rose $2.30, or 6.8%, to $36.35.
Multiple published reports suggested that ExxonMobil (XOM, Fortune 500) and another American oil giant, most likely Chevron (CVX, Fortune 500), have requested the U.S. government's clearance to make a bid for BP worth about $150 billion.
Spokesmen from both Exxon Mobil and Chevron said the companies don't comment on what they called rumors and speculation.
Shares of the U.S.-based oil companies edged slightly higher.
It was also reported that BP (BP) is looking to sell its stake in the United States' largest oil field, the Prudhoe Bay project in Alaska, to boost its clean up fund for the oil spill in the Gulf of Mexico.
The reports said BP is in talks with Houston-based oil and gas company Apache Corp. (APA, Fortune 500), and the sale would raise about $10 billion.
In response, Apache spokesman Bill Mintz said "We don't comment on speculation."
Shares of Apache fell 2.8%.
After hitting a 14-year intraday low of $26.75 on June 28, BP's stock has surged more than 27%. But shares are still down 42.8% since the Deepwater Horizon rig exploded April 20.
The British oil company has already suspended its dividend and said it will set aside $20 billion in an escrow account for spill-related costs.
Meanwhile, BP said Monday it has already spent $3.5 billion in containment, relief well drilling, grants, claims and federal costs for the spill.
The company is also making progress with the newest capping system, said BP exploration and production chief operating officer Doug Suttles during a technical briefing Monday.
He said the company has successfully installed the transition spool, which will allow BP to attach a containment cap later Monday.
Once the cap is in place, Suttles said BP will monitor the pressure and test the integrity of the containment well for at least 48 hours. 
| Index | Last | Change | % Change |
|---|---|---|---|
| Dow | 12,454.83 | -74.92 | -0.60% |
| Nasdaq | 2,837.53 | -1.85 | -0.07% |
| S&P 500 | 1,317.82 | -2.86 | -0.22% |
| Treasuries | 1.74 | -0.01 | -0.80% |
| Company | Price | Change | % Change |
|---|---|---|---|
| Bank of America Corp... | 7.15 | 0.01 | 0.14% |
| Sprint Nextel Corp | 2.62 | 0.09 | 3.56% |
| Cisco Systems Inc | 16.33 | -0.06 | -0.37% |
| Chesapeake Energy Co... | 15.81 | 0.23 | 1.48% |
| Ford Motor Co | 10.60 | 0.01 | 0.09% |
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