But Sam Younger, chief executive of the commission, told the Public Administration Select Committee during the same hearing that a "pretty significant" levy on the sector would be needed for such a scheme to work.
Both were responding to questions about funding from Alun Cairns, Conservative MP for the Vale of Glamorgan, during the latest PASC hearing into regulation of the sector and the Charities Act 2006.
Shawcross said the commission had examined the possibility of charging for filing accounts or for registration – an idea first discussed with the committee a year ago by his predecessor, Dame Suzi Leather.
He said the reasoning was to help the commission raise money. But at present, he said, any money raised would go to the Treasury, not directly to the commission, and a change to this situation would require primary legislation.
"We have to look at all alternatives," said Shawcross. "One suggestion is that charities will have to pay for their own regulation. That’s something we will have to look at, because the commission has to be properly funded to be effective.
"But it would be much resisted by charities. And it’s not going to happen immediately."
Younger said that charging for transactions such as filing and registration would fund the commission "only at the margins".
"If you were to do it comprehensively, it would have to be much more in the context of a levy on charities," he said. "When you run the figures, the levy that would be required is pretty significant and would run into great opposition."
He said that it would be expensive and difficult to collect fees, and that the commission currently had no mechanism for doing so.
Shawcross said the commission had considered a levy on all charities over a certain size.
"For example, the top 5,000 charities could pay £5,000 each, and that would get you £25m a year," he said.
The commission’s annual budget is falling from £29.3m in 2010/11 to £21.3m in 2014/15.
Shawcross said the regulator has also considered collecting a portion of Gift Aid, and said a levy of 2 or 3 per cent would be needed to fund the commission's budget. Charities received £1.08bn of Gift Aid in the year to March 2012.
Giving evidence to the same committee immediately after Shawcross and Younger, Nick Hurd, the Minister for Civil Society, said he expected that the government would still cover the bulk of the Charity Commission’s costs for the foreseeable future.
"This is an extremely difficult time to introduce the concept of additional charging to the charity sector," he said, but charities that "took up a lot of the commission’s time" could be forced to contribute to the commission’s costs.
"My personal view is that politically it would be quite wrong to move away from a position where the taxpayer funds the regulator," said Hurd. "I cannot see a very big shift. I’m not comfortable with the idea of adding to the cost burden of charities at this time."
Bernard Jenkin, chair of the committee and Conservative MP for Harwich and North Essex, said he felt that there was "something rather daft" about "the government funding charities with tax relief with one hand and then scooping it back to fund the state regulator with another".
He said he suspected that there was disagreement between the Cabinet Office and the Treasury about charging charities for registration. "It seems likely that the Treasury wants the money and the Cabinet Office wants to keep everything the same," he said.