The unpublished salary for the top post at the pound;8.2bn quango is being increased from pound;125,000 to pound;200,000 with "significant target-related bonuses" - in an effort to attract a top-flight industrialist with public-sector experience.
A founder member of the LSC's National Council, Mr Banks, 43, is seen as youthful and energetic as well as having the right credentials. He gets on famously with the current chairman and like-minded industrialist Bryan Sanderson, and he is a popular figure in the council.
From the start, Mr Banks took an active, high-profile role as chair of the LSC youth learning committee. And there was no let-up in his zeal when he quit as managing director of Coca-Cola UK to create his own food and drink enterprise, Big Thoughts Ltd.
He told FE Focus that creating his own company "gave me the opportunity to run my own show and has been - is - great fun".
Mr Banks made it clear that he had an equal passion for his work on the council but refused to comment on whether he was going for the top job.
However, colleagues and close acquaintances insist that Mr Banks is interested and is the right man for the job.
Asked whether the post would be too much for a man running his own company, one industrialist said: "He's a good delegator. That's what makes him a good chief exec. He'd find someone good to run the company."
The 16-page information pack sent to applicants for the LSC chief executive post stresses that "it is vital shehe is not an 'organisation bureaucrat', in other words motivated by running an organisation as an end in itself".
Those who know Mr Banks say he is definitely not an organisation man and that bureaucracy is anathema to him.
"He is definitely a no waffle merchant," said one associate.
Inevitably, people spoke of him "putting the fizz into the council" and say "like Coke, Chris is the real thing".