BP Chief Executive Bob Dudley, who has been criticised by investors for the difficulties encountered in executing the deal, said he was optimistic that it would be concluded but declined to express a view on whether the deadline would be met.
I think we will find a resolution to this over time, Dudley told Reuters in an interview on the sidelines of a conference in St Gallen on Friday.
Analysts said the opacity around the situation made it impossible to know whether Rosneft would agree to extend the deadline but noted a lot of elements had to be agreed before the share swap could be concluded.
BP and Rosneft agreed to a $16 billion share swap and an exploration venture aimed at unlocking potentially 40 billion barrels of oil in the Russian Arctic Sea in January.
The deal, which was announced with great fanfare by BP, was supposed to mark a turning point in the London-based oil giant's fortunes after the Gulf of Mexico oil spill.
But BP's oligarch partners in its Russian joint venture, TNK-BP
AAR, the group which represents the four oligarchs that own a half-share in TNK-BP, secured an injunction blocking the Rosneft tie-up, unless BP convinces Rosneft to execute the Arctic deal through TNK-BP.
However, it is unclear if Rosneft, Russia's largest oil producer, will agree to working with TNK-BP. The Kremlin-controlled company has previously said it saw no sense in partnering with TNK-BP, which has no offshore experience.
The agreement, sealed in January, to swap a 5 percent stake in BP for a 9.5 percent stake in Rosneft expires on Monday, having already been extended once already.
The two stakes were valued at around $8 billion at the time the deal was signed but BP's shares dropped due to fears about the dispute with its TNK-BP partners, while Rosneft's shares have risen, creating a $1.4 differential between the value of the two stakes currently.
BP investors fear that Rosneft may demand a redraft in the terms that could see BP paying, either in cash or shares, another $1 billion or more to complete the deal -- something which would further dent Dudley's credibility.
(Editing by Patrick Graham)