It is unclear whether the new proposal covers the Arctic exploration planned under the previous agreement.
Meanwhile Russian President Dmitry Medvedev has criticised the way the original deal was put together.
BP had earlier said that it would continue talking to Russian oil giant Rosneft over a share swap.
Analysts suggest Rosneft may now be talking about its Arctic assets with other major oil firms that have deep-sea drilling expertise, notably Exxon, Chevron and Shell.
Shareholders' interests BP's Arctic exploration and share swap agreements with Rosneft were sunk after AAR, the Russian business partners in BP's earlier Russian TNK-BP joint venture, successfully argued that the tie-up broke previous agreements BP had signed with them.
The formal deadline for BP to consummate its agreement with Rosneft was reached on Monday without BP finding a way past the impasse with AAR.
"As a result of the negotiating process between BP and AAR, Rosneft has received proposals which go beyond the previous agreements and do not require the extension of the deadline (for the share swap) which expired on May 16, 2011," said Rosneft in a statement.
Dmitry Medvedev President of RussiaWe should have conducted more careful due diligence inside the government”
"Considering these proposals, Rosneft will above all be guided by the need to respect the interests of its shareholders and the necessity of fulfilling its licensing agreements on the Arctic shelf, where the company is continuing active work."On Tuesday, BP said it would continue to try to find a way for the three parties to reach an agreement.
The original deal between BP and state-owned Rosneft would have given the UK oil giant access to the potentially lucrative oil reserves in the Russian Arctic.
"In recent months, BP has conducted detailed negotiations with AAR and Rosneft to seek a reasonable and businesslike solution that would allow the agreements to proceed to the satisfaction of all parties," BP said.
"Such a solution has not been found at this time, although talks will continue."
The fundamental problem was that the billionaires and Rosneft, which is an arm of the Russian state, don't trust each other”
Mikhail Fridman, chairman of Alfa Group, the group of billionaires behind AAR, said: "AAR also sees significant benefit to developing co-operation with Rosneft within the framework of the TNK-BP shareholder agreement, and we plan to continue discussions about any potential collaboration among BP, Rosneft and AAR."Exclusivity agreement The Russian president weighed in on the negotiations, saying that BP and Rosneft should have paid closer attention to BP's earlier agreements with AAR.
"We should have conducted more careful due diligence inside the government... and this, I think, was not done," said Mr Medvedev in an implicit criticism of Russian Deputy Prime Minister Igor Sechin, who put the deal together on the Russian side.
Under the BP-Rosneft deal, which was signed in January, the Russian firm would have taken 5% of BP's shares in exchange for approximately 9.5% of Rosneft's shares.
But AAR said that the deal broke an existing exclusivity agreement between it and BP.
The AAR consortium won a High Court injunction in London in February.
It put the deal on hold until the dispute could be resolved by arbitration, and in March an arbitration panel upheld AAR's complaint.
Last week, arbitrators ruled that BP and Rosneft would be allowed to swap shares if the Arctic operations were carried out under TNK-BP, instead of BP itself.