We had an offer from BP ... about its agreements with Rosneft. For the company, obviously, the partnership would be interesting, Maxim Barsky told reporters on a visit to an oil-rich West Siberian region.
The company is reviewing the offer and we will present it at the board of directors on February 18.
He gave no further details of BP's proposal.
The British major and Rosneft, Russia's biggest oil producer, earlier this year struck a share swap deal which will see them jointly explore the Arctic for oil.
The deal drew opposition from AAR, the consortium of Russian shareholders in TNK-BP, who said it violated their shareholder agreement and secured a London court injunction to freeze the deal.
Under a shareholders' agreement between BP and a Moscow-based consortium of investors with whom it evenly divides control of No. 3 Russian oil producer TNK-BP, the TNK-BP board has right of review over BP's other Russian activities.
BP declined to comment on Barsky's remarks.
We haven't heard about these proposals and we don't know what are they about, a Rosneft spokesman told Reuters.
Barsky said he hoped that differences between BP and Russian shareholders in TNK-BP would be soon resolved.
(Reporting by Olesya Astakhova; Additional reporting by
Vladimir Soldatkin in Moscow and Sarah Young in London; Editing by Hans Peters)