Mr Byers said he was "particularly interested" in the suggestion, one of a number of options raised at a meeting yesterday with some of the newer, smaller mortgage industry players, such as egg and First Active.
A DTI official said Mr Byers was considering a crackdown on the redemption charges triggered when people move home, but keep their mortgage with the same company.
Tony Ward, managing director at First Active, said that those at yesterday's meeting had been "unified against the old guard" in demanding action to simplify and limit redemption penalties.
There was particular concern on "overhanging" redemption penalties, where the homeowner is tied in to a particular mortgage for longer than the lender is bound to a particular interest rate.
Mr Byers is trying to push the industry into what he claims is a better deal for the consumer, and officials say he will pursue the ideas at a second "mortgage summit" with the biggest lenders next month. Officials say that if the industry fails to agree the practices voluntarily, the Government could legislate.
Yesterday Mr Byers said he was pleased many mortgage lenders recognised the need to offer a fair deal. "This [a mortgage] is the most important financial transaction that most people enter into and it is vital that they are not confused by smoke and mirrors. Progress has been made but we shall continue to keep up the pressure on lenders," he said.
Last month, Mr Byers introduced measures to standardise the calculation of interest rate payments across the industry. The move followed the first large-scale meeting with lenders in October.