They will be offered the opportunity to take some of the negative equity with them onto a fresh loan for a new property.
A total of four banks hope the move will help breathe life into the stagnant property market.
It is understood that AIB, Ulster Bank, EBS and KBC Bank are in talks with the Central Bank and regulators to offer the new mortgage product.
Already Bank of Ireland and Permanent TSB have offered a limited option to take a portion of what's owed on a current home onto a new mortgage.
Up until now, those with a mortgage and in negative equity have been prevented by their banks from selling up to a bigger home.
This is despite the fact that many are still on a salary that could meet payments on a new mortgage if they were allowed to transfer some of the negative equity onto a new loan.
The news comes on the back of an announcement by Ulster Bank whereby customers would be entitled to keep their low-cost tracker mortgage with them when they move.
Trackers had become like 'golden handcuffs' for 400,000 householders who were disinclined to trade up or down for fear of losing the lucrative rate.
Jim Ryan, Head of Branch Banking, said that the initiative was to help customers move house by taking the tracker mortgage with them.
Frank Conway of the Irish Mortgage Corporation said that most people are eager to be freed from the "trap".
They have already accepted that they will sell their property for less than what they paid for it.
"Most people that would be looking to move would be doing so for employment reasons or family reasons," he told the Herald. "I don't think they would be overly concerned with negative equity amounts."
Under the new rules brought in by banks to help with the negative equity nightmare, homeowners would be able to tack the balance they owe on to the new mortgage.
Homeowners who qualify for the new deals would still owe money to the bank if they sold.
And the deals will be only be offered to those with good earning capacity.
Anyone who has missed a payment on their mortgage will be excluded from the scheme.
DAN WHITE, P14-15
and it will be limited to those who are considered by the banks to be able to meet the repayments.
Analysts said that it doesn't help a huge number of individuals who are struggling with their repayments and it also limits the amount of negative equity that can be carried on.
Mr Conway said that banks are only working in circumstances where there were no arrears and this is nearly always driven by job security,
"It is a very difficult call but it is separate issue. Banks will need to look for a different solution to this," he told the Herald.
"What they are trying to avoid doing is support something where someone is having difficulty paying."