The department store chain, which has 140 stores, plans to try out several schemes, putting pressure on other high-street shops such as Topshop, Next and Bhs to do the same.
The move follows Marks & Spencer's decision last week to introduce a 5p charge throughout its food stores and to offer its customers free "bags for life".
A spokesperson for Debenhams said: "We are working on several proposals, including offering reusable cotton bags and charging for carrier bags. We are about to conduct trials in a number of stores to gauge customer reaction."
Lisa Williams, head of investor relations at Debenhams, told the Mail that removing free bags was more difficult when dealing with fashion products than food but that something had to be done.
She said: "We all realise we have to do something. We are really committed to reducing our impact on the environment."
As many as 13bn plastic bags are given away free to UK shoppers every year and they take an estimated 1,000 years to decay.
Last week, Prime Minister Gordon Brown threw his weight behind the "banish the bags" campaign, warning supermarkets that if they do not voluntarily cut down on the number of plastic bags given away they will be forced to do so.
B&Q, the DIY chain, is expected to bring in a 5p charge following successful trials in Scotland and the North East.
Supermarkets in Jersey and Guernsey yesterday agreed to start charging customers 5p a bag from May. It is expected to halve the number of plastic carrier bags given out in the islands, currently 40m a year.
Ikea, Aldi, Lidl and Netto have imposed charges for several years.