We had an offer from BP ... about its agreements with Rosneft. Obviously a 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.
TNK-BP's involvement in the partnership deal struck by BP and Rosneft to swap shares and jointly explore the Arctic for oil could placate AAR, the Russian consortium which owns half of TNK-BP and which has so far opposed the BP-Rosneft tie-up.
But Barsky's remarks are at odds with Rosneft Chief Financial Officer Peter O'Brien, who scoffed at the prospect of TNK-BP as a potential partner.
Rosneft told Reuters on Friday it was not aware BP had made an offer to TNK-BP.
We haven't heard about these proposals and we don't know what are they about, a Rosneft spokesman told Reuters.
BP declined to comment on Barsky's remarks.
BP Chief Executive Bob Dudley floated the idea that TNK-BP could be included in the Arctic exploration venture when the British oil major unveiled results on February 1.
AAR believes BP's partnership with Rosneft violates their shareholder agreement and secured a London court injunction to put the deal on hold.
Barsky said he hoped differences between BP and Russian shareholders in TNK-BP would be soon resolved.
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.
Industry sources have said the Russian partners are trying to get a piece of the action in the Arctic or to partner with BP abroad, as TNK-BP's Siberian operations are growing slowly and face a peak oil scenario going into the 2020s.
Shares in BP, which have fallen 5 percent since the company announced the deal with Rosneft in mid-January, were down 0.5 percent to 474.2 pence at 1320 GMT, underperforming Britain's blue-chip index of companies which was 0.1 percent lower.
(Additional reporting by Vladimir Soldatkin; Editing by Hans Peters and David Hulmes)