The paper reports that Jenkins made the comments in a speech to the Institute of Chartered Accountants in England and Wales on Thursday night.
Maturity transformation is where banks take short-term deposits - current accounts, easy access savings accounts - and use it to fund longer-term products such as mortgages. This is central to how retail banks make their money, profiting between the difference in interest rate offered to savers and charged to borrowers.
The Telegraph report doesn't specifically say how this feature will be eroded but points to the rise of marketplace lenders like RateSetter and Funding Circle that match savers and borrowers directly, cutting out the banks who sit in the middle.
City AM reports that the end of maturity transformation is only one of several predictions made by Jenkins in his speech. Others include deep cuts to branch numbers and banking staff, more automation, more failure, and power shifting to the consumer.
All the changes are being bought about by the rise of fintech - financial technology. New startups are challenging banks to rethink the way they structure their products and deliver them to customers.
Jenkins, who was CEO of Barclays from 2012 until last year, has made these predictions before. Last November he made a speech predicting banking was approaching an "Uber moment" that would see the industry transformed by technology.
Perhaps unsurprisingly given all these predictions, Jenkins is trying to get into fintech himself. The banker has reviewed 100 fintech businesses and met with 50. He is reportedly mulling either joining one or starting up his own venture.