The Elgin platform in the North Sea was evacuated after Total confirmed a significant natural gas leak about 150 miles off the coast of Aberdeen at the end of March.
Total announced plans to pump drilling mud on the well leaking natural gas in the North Sea and drill two relief wells below the platform.
Philippe Guys, managing director for regional operations at Total, told Scottish daily newspaper the Press and Journal that responders should be able to "kill the well by the end of the month.
"We are working hard and if all goes as planned we envisage by the end of this month we should be having control of the well," he was quoted as saying.
Visual inspection of the site confirmed that gas was leaking from the platform and not underwater, Total said. Equipment shipped by Texas management company Wild Well Control arrived in Scotland during the weekend to respond to the leak.
The Scottish government had said there was a "minimal" threat to the environment from the leak.
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