The shake-up could include extending a text alert service that warns customers when they are a day away from going into the red, and letting those with multiple accounts automatically move money around to avoid overdraft charges.
Coin machines will also be piloted in some branches to enable customers to count and credit loose change into their accounts.
Ashok Vaswani, head of Barclays' retail and business banking, told The Daily Telegraph: "I'm going through the business with a fine toothcomb. We want to de-risk the business and clean up any sins of the past."
The measures are among 2,600 ideas that it received after asking customers for suggestions to make everyday banking easier.
They come just a week after an ethical scorecard ranked Barclays at the bottom of a list of 100 banks, with just four out of 100 points.
The bank said it will work on a new overdraft policy over the next 90 to 120 days. It currently charges most of its current account customers £22 every five working days that they are in breach of their first overdraft limit.
However, parenting group Netmums has warned the move risks the modern day equivalent of having your lunch money stolen.
Netmums founder Siobhan Freegard said: "There are already some concerns about young children using mobiles and official Government guidance is not to let youngsters use them until they are 16. Adding the ability to transfer money could see some kids suffer bullying as well as financial loss."