The Washington-based development bank seems reluctant to reengage in a country where it stopped all new projects in 2005 in compliance with the international sanctions imposed over Iran's nuclear program.
But since those sanctions were removed in January in the wake of a nuclear deal between Tehran and world powers, the World Bank has not shifted.
"We're following the situation very closely ... we don't have any specific plans yet," said World Bank President Jim Yong Kim.
Iranian authorities haven't made any requests to the Bank for help.
But the reasons for the Bank's reticence can be found elsewhere -- at the intersection of the economy and geopolitics and the desire not to offend the United States.
The United States, the largest World Bank shareholder, and the primary supporter of Kim, an American, sends mixed signals on just what is acceptable in doing business with Iran.
Crucially, while sanctions tied to Iran's nuclear program were lifted, US sanctions applied for Tehran's alleged support for terrorism and human rights violations remain in place.
In theory, those remaining sanctions don't prevent the World Bank or other international financial institutions to engage with Iran, a spokeswoman for the US Treasury told AFP.
But, she added, the US representative at the Bank has other constraints.
"Current legislative mandates direct the United States executive director to vote against World Bank loans to Iran," she said.
Theoretically the Bank could work around the problem and finance development projects -- in the areas of transportation, energy and infrastructure, for example -- in a country where poverty has soared as a result of the economic embargo.
But the fact is, a frown on the face of the world's top power and the Bank's largest shareholder cannot be ignored.
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"There's certainly a political risk for the World Bank to be associated with Iran, as Congress could respond very negatively, said Jacob Kirkegaard, an expert at the Peterson Institute for International Economics.
Controlled by Republicans opposed to the Iran nuclear agreement, Congress has powerful leverage: it could block the release of funds the US has promised the World Bank for helping the poorest of countries.
The sanctions still in place constitute another sizeable obstacle.
"In a situation where you're going to finance projects that will be open to international competitive bidding, the fact that there are still US sanctions is clearly a complication," said former World Bank official Paul Cadario.
On the one hand, the Bank has to make sure that its projects are in no way associated with Iranian individuals and companies on the US blacklist.
Companies, on the other hand, could be deterred from bidding on a World Bank-financed project in Iran "because payments could go through the US (financial) system and expose them to the American sanctions," said Cadario, now at the University of Toronto.
The World Bank has been in that situation before. In 2007, it had to suspend payment of $5.4 million linked to a pre-2005 Iran project after discovering that the funds passed through Iran's Melli Bank, which was targeted by US sanctions.
Beyond the World Bank, the return of international financial institutions to Iran after the nuclear sanctions were dropped is also uncertain, to the great displeasure of officials in Tehran.
Iran's central bank governor recently pointed to the reticence of European banks to engage with the country in fear of falling afoul of US sanctions.
"They have been asked not to work with Iranian banks, and they're afraid," Valiollah Seif said at a forum in Washington.
One consequence is that Iran has started turning away from the West-dominated World Bank toward alternatives.
Iran is one of the founding members of the China-led Asian Infrastructure Investment Bank and is seeking to join the New Development Bank backed by the BRICS nations of Brazil, Russia, India, China and South Africa.