Nick Hurd, the Minister for Civil Society, has called the Gift Aid system "archaic" and said that he sees the future of the system online.
He said Gift Aid was a Treasury matter and pointed out that he was not a Treasury minister, but said: "I will certainly be making sure this report will be given full consideration by the Gift Aid Forum."
The forum, a discussion group involving major charity umbrella bodies and the Treasury, is due to meet on Thursday.
"As minister who is champion of the sector inside government, I’m happy to work with you on modernising it and working towards taking it online, as that does seem to be the future," said Hurd.
John Low, chief executive of the Charities Aid Foundation, which commissioned the ResPublica report, said young people were using new technologies to donate. Without an online claim system, they could not claim Gift Aid and the tax recovered would fall, he said.
He said taking Gift Aid online presented the opportunity to "harvest the enthusiasm of a new generation to give to charity". But he said that it would need government backing to make it work.