The Stock Exchange recently told the headhunting firm Heidrich Struggles to rethink after months of fruitless searching for an external candidate suitable to lead the exchange into a new era.
Ms Barker is generally perceived to be first-rate and it is believed that some of the exchange's appointment committee would now be more prepared to consider an internal candidate to replace Peter Rawlins. He resigned last March after the fiasco over Taurus, the paperless share settlement system.
Ms Barker, who declined to comment on the job, has told friends that she is undecided about whether to put herself forward. She is afraid that if she gets the post it will have been almost 'by default'.
City observers have noted that the Stock Exchange, following the Taurus debacle, has been left with little definite idea of its role. This has been one of the reasons behind its difficulty in finding a suitable replacement for Mr Rawlins. Ms Barker joined the exchange as chief financial officer in 1990, having been poached from CT Bowring.
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