The Times report suggests Vincent de Rivaz has staked his credibility on getting the plans off the ground, with the EDF boss ready to quit the UK if the plans fail to come to fruition.
The news comes after only last week, David Hall, the deputy leader of Somerset County Council, spoke out to reveal there were no imminent indications that talks were failing.
He said: "The main message we're receiving from all sides is, 'Don't panic'.
"This is a very complex and important negotiation because it potentially fixes electricity prices a long way into the future. That's going to be a challenging negotiation."
EDF's plans for the construction of the country's first nuclear power reactors in over two decades have been besieged with problems from the outset.
Initially, proposals were delayed in the face of financial problems in the firm's native France, leading to question marks being raised over whether the project would go ahead. This was joined as well by other issues including EDF's partner in the project, British Gas owner, Centrica, pulling out of proposals.
Although rumours persist that China Guangdong Nuclear Power Holding Co may be brought in as a new partner for the project, of bigger concern is the fact EDF is currently at loggerheads with the UK Government over the money it will receive from the government for the power it generates from the sites.
While EDF is after a deal over 40 years which will guarantee at least Â£95 a megawatt-hour, the government is holding out for a deal offering customers the best value for money.
EDF Energy is one of the 'Big Six energy' suppliers in the UK.Â It is currently working alongside the government as part of its Green Deal. Under the scheme customers can receive subsidies on a number of measures to improve energy-efficiency in the home.
These measures include the fitting or replacing of a more energy efficient boiler, solar panels and also loft and wall insulation.
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