But Shell has only received acceptances from five per cent of shareholders and analysts expect the takeover battle has longer to run.
Shell and Thai firm PTT have been vying to acquire Cove in recent months, lured by its stake in huge gas fields discovered off the coast of Mozambique.
PTT trumped Shell's $1.8bn offer with a $1.9bn bid in May. But shares in Cove have been trading well above PTT's offer on investor expectations that a bidding war will occur.
Cove is expect to announce the discovery of more gas on Monday.