It follows criticism of the performance and policies of the Welsh government's investment body Finance Wales.
The Development Bank for Wales was proposed in a review last year by the economist Dylan Jones-Evans.
It would take over part or all of Finance Wales, which he said was "not fit for purpose".
Finance Wales was set up in 2001 to lend money to or buy shares in Welsh companies.
But last year's review said it was too focused on generating profits rather than helping businesses and developing the Welsh economy.
The report said there was confusion over the bank's exact role and concerns about the cost of loans to small firms.
Prof Jones-Evans, an academic at the University of the West of England, said Finance Wales was offering higher rates of interest on borrowing than it needed to under EU state aid guidelines.
Plan for the new bank emerged on Wednesday as an investigation by BBC current affairs series The Wales Report revealed that investments from Finance Wales' main European fund had only resulted in 20% of the jobs they were expected to create.
The £150 million JEREMIE fund was established in 2009, draws money from European sources and the Welsh government, and comes to an end in September 2015.
Finance Wales was given an initial target of creating 15,000 jobs using this fund, later reduced to a target of getting 10,070 people into work.
With a little over 18 months left, the latest figures show 1,991 jobs have been created with most of the fund invested.
By Brian MeechanBBC Wales business correspondent
Prof Jones-Evans's report into how Welsh businesses access finance found there was a £500m shortfall between what firms need and what banks will provide.
Finance Wales is owned and funded by the Welsh government. Its aim is to help small and medium sized companies be able to borrow.
The report said it was too focused on getting high returns on its investment through interest rates and fees rather than stimulating growth in the economy and creating jobs.
The Wales Report has uncovered figures which show the organisation has created only 20% of the jobs target set for its main European fund.
Finance Wales says its loans are often high risk and therefore they expect a return on that money.
But the independent report said some or all of its operations should be taken over by a new development bank.
While Finance Wales has smaller funds and has created and secured other jobs, the employment results for JEREMIE represent around 20% of a target that was already reduced.
In a written statement on Wednesday afternoon, Mrs Hart confirmed she would be "exploring further the proposal for a development bank for Wales".
Mrs Hart said she had asked Professor Jones-Evans "to lead a further review that will explore this concept in more depth and provide me with a report on his findings".
She added that the terms of reference were still being agreed but he would "explore the potential mission, role and operations that such an organisation could undertake; the legal and state aid framework required to establish and operate; the necessary skills, experience and costs; and the relative risks and rewards."
Answering questions from AMs later, Mrs Hart said a "lot of the business community are happy" with the support from Finance Wales.
Ms Hart added that "there are issues" but that she had been "transparent" and that there was a need to carry out further work.
The Conservatives' shadow business minister Nick Ramsay said Finance Wales "has done some things well" but "other things badly", such as charging high interest rates to companies "without justification" and that "Finance Wales clearly has to go."
Ms Hart replied that some Welsh businesses would not have been successful without support from Finance Wales.
Earlier, the Federation of Small Businesses welcomed the prospect of a new development bank.
Iestyn Davies from FSB Wales said Prof Jones-Evans's report had "shone a stark light on Finance Wales, and the inflated interest rates that it has been charging our members".
"We are very much in favour of reform to Finance Wales to ensure that it provides affordable loans to small business and is properly accountable with a far higher degree of transparency and opportunity for scrutiny than exists at present.
"We believe that the notion of a Development Bank of Wales is worthy of serious consideration, and we welcome a review into how such a bank would operate in practice."
Plaid Cymru's economy spokesman Rhun ap Iorwerth said: "Access to finance has consistently been cited as a barrier to growth for many SMEs (small to medium size enterprises) and much more needs to be done to tackle this problem.
"That's why Plaid Cymru proposed to establish a new body, owned by the public but at arm's length from government to lend money to small businesses at competitive rates and to offer finance services.
"A Welsh public bank is the boost that Welsh businesses need and Plaid Cymru will continue to make the case for it."
But the Liberal Democrats said it was important that Mrs Hart "keeps her options open".
Their economy spokeswoman Eluned Parrott said: "The Welsh Labour government's record of acting as financier for businesses is mixed at best.
"The recent Access to Finance Review identified shortcomings in the government-backed Finance Wales.
"Having spoken to many businesses across Wales, Finance Wales seems to be offering higher interest rates and less favourable terms compared to commercial banks - this is not a way of encouraging businesses in Wales to grow."
For more about Finance Wales, see The Wales Report on BBC One Wales at 22:35 GMT on Wednesday, 29 January.
A development bank for Welsh businesses could be on the cards as Economy Minister Edwina Hart goes ahead with plans to see how it would work.