Jenkins has not set the 40,000 role reductions as a formal target but floated the idea of large-scale job reductions in meetings with investors that took place after the bank published its results last month.
Sky News said Jenkins had told investors he could see the bank employing 100,000 staff worldwide compared with 140,000 now.
When he fronted the bank's results in February in his first set-piece presentation since taking the helm in September, Jenkins outlined plans to cut 3,700 jobs as it pulled back from continental Europe to focus on Britain, the US and Asia. About 1,600 roles had already been cut from the investment bank by the time he made last month's announcement, which was accompanied by a pledge to pull out of food speculation and major tax avoidance schemes.
A former head of Barclaycard and the retail bank, Jenkins was appointed chief executive following the sudden departure of Bob Diamond in the wake of the £290m Libor-rigging fine. He has pledged to change the culture of the bank, linking bonuses to new values of respect, integrity, service, excellence and stewardship.
In meetings with shareholders, he is said to have discussed the idea of turning the bank into a company focused on service for customers and becoming more efficient.
Among the other ways Barclays intends to clean up its culture following the Libor fine was through a review by the prominent lawyer Anthony Salz, who is due to complete his report shortly. A former head of the Freshfields law firm, Salz began his review before the appointment of Jenkins and has sought assurances that the report will be published.
Evidence that Jenkins has begun to make changes to the way staff are paid will be sought when the bank publishes its annual report in the coming days. Under the guidance of the new chairman, Sir David Walker, the bank is to provide more detail than in the past about its high earners by publishing pay in bands, which is expected to show that as many as 600 staff took home more than £1m last year.
Walker had been asked by the Labour government to review City culture after the 2008 banking crisis and advised that more information about bankers' pay was disclosed, in bands above £1m.
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