Natural gas is leaking at a rate of around 7 million cubic feet per day from near the top of the Elgin platform.
A spokeswoman for the company was quoted by the Scotsman newspaper as saying "significant progress" was made in plans to stop the natural gas leak, first reported at the end of March.
The company said it deployed two rigs to the area in preparation for the drilling of two relief wells.
"Several further helicopter flights may be required ahead of the positioning of a well intervention support vessel alongside the Elgin complex," the company said it its latest update.
The Scottish government said the risk to the environment from the natural gas leak was "minimal." Edinburgh is leading an environmental task force to monitor the incident alongside the British Department of Energy and Climate Change.
Natural gas isn't leaking underwater, the French energy company said.