Michael Jenkins, Liffe's present chief executive, who helped to mastermind the recent merger with the smaller London Traded Options Market, is due to step down shortly after 11 years.
Liffe is second only to the Chicago markets in trading financial futures and stock options.
A Liffe sub-committee will meet soon to consider a shortlist of candidates.
Mr Thorpe's candidature is believed to be supported by Liffe members, who back the appointment of someone with a strong regulatory background. But no firm decision has yet been taken and, amid considerable behind-the-scenes lobbying, others favour giving the job to a captain of industry.
Mr Thorpe is deputy chief executive of the Securities and Futures Authority but has spent the past 10 months on secondment to FOX. He was put in after a series of scandals rocked confidence in the market.
A New Zealand-born barrister, Mr Thorpe is a former deputy commissioner for securities in Hong Kong, where he was seconded to reform the Hong Kong Futures Exchange, which suffered great problems in the October 1987 crash.Reuse content