Norwegian company Seadrill is the only bidder left in the running for Scorpion Offshore, having raised its offer twice and forcing New York-listed Ensco International to pull out from the race.
Ensco said it would abandon its takeover attempt after Seadrill advisor Pareto Securities said Seadrill would increase its bid to Nkr40.50 ($6.26) per share.
On Friday, the Norwegian driller raised its bid for Scorpion twice.
The companies had been engaged in a bidding war for Scorpion Offshore.
It was still unclear if Seadrill's conditions of reaching 50% ownership in Scorpion had been fulfilled.
Ensco launched a recommended tender offer of Nkr39.50 per share on Thursday aimed at winning control of Scorpion Offshore and trumping an earlier bid from Seadrill, which owns about 40% of Scorpion.
Seadrill raised its bid twice, with an all-cash offer valuing Scorpion at $567 million. Ensco advisor Arctic Securities said Ensco would not go beyond Nkr40 per share.
While oilfield services deals have hogged much of the attention in the past few quarters, bankers and investors are increasingly scanning the M&A horizon for offshore drilling rigs as that industry steadily pulls out of a slump.
Earlier this month, Seadrill, controlled by Norwegian shipping tycoon John Fredriksen, launched an offer of Nkr36 per share, with the world's number two deep-water driller saying it wanted to try take 100% of Scorpion.
Seadrill shares closed down 3.4% in Oslo trade on Friday, while Ensco's fell by 3.7% in New York at 1652 GMT. Scorpion shared closed at Nkr40 in Oslo trade on Friday
Ensco was also advised by investment bank Goldman Sachs .