They are discussing help from rich countries and from Gulf nations.
They say the idea has been well received by potential contributors and hope to have the first funds paid out in four to six months.
The arrangement under discussion is one in which the Bank would make loans to Jordan and Lebanon, with aid donors covering at least some of the interest costs.
Millions of refugees are now in countries bordering Syria. The largest number are in Turkey, but it is the much smaller economies of Lebanon and Jordan that face far greater financial strain.
In Lebanon the number is equivalent to 30% of the population. In Jordan the figure is 20%.
The cost to government budgets comes from the 85% of the refugee population that live in normal housing rather than camps, where the costs are borne by the United Nations.
For those not in camps there is a cost in terms of healthcare and education. There is also water supply and electricity. Even if they pay the bills these prices are often subsidised so the presence of the refugees adds to the total cost to the government.
By hosting the refugees the countries concerned are providing what a World Bank economist called a "global public good". So there is a willingness to help with the cost.
But Lebanon and Jordan are classified as middle income countries. The World Bank can`t provide them with grants or cheap loans. It can only do that for low income nations. For middle income countries it can lend but at an interest rate that in essence covers the Bank`s own borrowing costs.
Lebanon and Jordan are reported to be reluctant - understandably, you might say - to pay interest for dealing with a problem not of their own making.
So the World Bank is instead proposing to provide the loans while aid donor nations ease the financial burden by covering some of interest payment costs. It`s not as direct a way of helping as grants would be, but it could make a significant difference.
The likely contributors to any such funding are the G7 - the largest developed economies, Gulf states and some smaller European nations.
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