The bank's current contract is in the first year of a three year tie-up that runs until the end of the 2015-16 football season.
Members of Barclays' management are concerned that rapid inflation in sports sponsorship costs will mean a much higher amount will be demanded next time, the Sunday Telegraph reported.
Barclays has been the sponsor of the Premier League since 2004 – and its credit card division, Barclaycard, had previously sponsored the competition from 2001. The bank paid £120m in 2012 for the present rights, 50% more than for the previous deal, which cost £82m.
In December, Barclays said it was pulling out of sponsoring Boris Johnson's bicycle hire scheme in central London as part of a wider review.
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