David Hainsworth, health, safety and environment manager for Total, told BBC Newsnight Scotland: "The flare is still alight on the main production platform, however the wind is blowing the gas plume in the opposite direction away from this flare.
"We know the weather forecast is such that the wind direction remains the same for the following five to six days and we're evaluating options to extinguish this flare."
Total said is was taking at least one rig out of use elsewhere to make it available if a relief well is need. It was also assessing whether it could intervene on the platform to "kill" the well.
However, Dr Martin Preston, marine pollution specialist and honorary research fellow at the University of Liverpool, told BBC Radio 4's Today programme there was a danger that the flare could ignite the flammable gas.
He said it would be unsafe to approach the platform until the flare is put out and that the French oil company may have no option but to drilll relief well that could take up to six months. Gas leaked uncontrolled on Tuesday at an estimated rate of 200,000 cubic metres a day, Mr Hainsworth said, based on the gas plume above the platform.
"If that finds a source of ignition, there will be a fire," he said.
A shipping exclusion zone was in place two miles around the platform, about 150 miles east of Aberdeen, and three miles around for aircraft. Firefighting ships were on standby.
Total E&P UK, which operates the Elgin platform, said it was taking "all possible measures" to try to identify the source and cause of the leak and to bring it under control.
Shell has reduced its workforce on two offshore installations close to the Total platform as a precaution. Around 85 staff have been taken off the company's Shearwater platform and the nearby Noble Hans Deul drilling rig, leaving a workforce of 117 people.
Shell also said it has brought forward plans for maintenance at Shearwater and is shutting down production in a "controlled manner".
A sheen on the water is present near the platform, estimated to extend over 1.85 square miles and measure between two and 20 tonnes in volume.
Total said its preliminary assessments indicate there has been no significant impact on the environment because of the leak.
Offshore union RMT welcomed the quick evacuation of the platform but warned there could still be serious consequences.
RMT offshore organiser Jake Molloy said: "Total acted very swiftly in getting everyone off but the potential still exists for catastrophic devastation.
"If the gas cloud somehow finds an ignition source we could be looking at complete destruction.
"This is an unprecedented situation and we really are in the realms of the unknown but the urgent need now is to find a way of stopping the flow of gas."
The Scottish Government said it is monitoring the developments.
Total E&P UK said it has met with the Secretary of State's representative, the Health and Safety Executive, the Department of Energy and Climate change, Marine Scotland and the Coastguard.
On Tuesday, Total's shares fell 6pc in Paris, wiping more than €5.5bn (£4.6bn) off the company's value and analysts said a worst-case scenario could see costs for Total running to billions of dollars.
Production from Elgin and the connected Franklin site, which has also been shut, account for about 3pc of the UK's gas supply, the Department of Energy and Climate Change said.
Stuart Joyner, Investec analyst, said a relief well could cost $50m, but that could be a "rounding error" in the context of a worst-case scenario bill, which he said potentially "could run into multi-billions of dollars".
The exact cause of the leak has still to be confirmed but Mr Hainsworth said workers at Elgin on Sunday had reported "a spray of liquid followed by a gas release" from a well casing.
The well had ceased production a year ago when it was plugged at its reservoir source, 6km below ground. Workers spotted changes to the pressure in its outer casing weeks ago and had been in the process of pumping in heavy mud to "kill" the casing on Sunday.
Gas is thought to be entering the casing from another, non-producing reservoir 4km underground, Mr Hainsworth said. Total did not yet know the capacity of this reservoir but in a "dream" scenario it could simply "run itself out".