Germany, France and the Netherlands are among the member states that have expressed support for the idea.
The European Union is under mounting political pressure to label Iran's Revolutionary Guard as a terrorist group over the paramilitary force's reported involvement in the crackdown on the anti-government protests that have swept the country since the killing of Mahsa Amini.
Germany, France and the Netherlands are among the member states who have mooted the possibility, while the European Parliament passed a resolution calling for the bloc to make the designation.
European Commission President Ursula von der Leyen has also backed the idea.
"The reaction of (the) Iran regime is atrocious and horrible and they are trampling over fundamental human rights," von der Leyen said last week while attending the World Economic Forum in Davos.
"We are looking indeed at a new round of sanctions and I would support also listing the Revolutionary Guards (as a terrorist organisation). I have heard several ministers asking for that and I think they are right."
Officially called the Islamic Revolutionary Guard Corps (IRGC), the group was set up by Ayatollah Khomeini after the 1979 revolution to protect Iran's newly-established Islamic system from internal and external threats, particularly foreign attempts to effect a regime change.
Since then, the IRGC has operated independently from the country's regular army, expanding its ranks, political influence and economic might in close association with Supreme Leader Ali Khamenei.
The IRGC is split into five branches: the ground forces, an air force, the navy, the Basij – a volunteer militia that represses dissent and polices moral codes –, and the Quds Force – a secretive intelligence service that conducts operations in other countries, often supporting armed groups.
Overall, the Guards are estimated to have between 150,000 and 230,000 troops under their joint command and have been described as "one of the most powerful paramilitary organisations in the Middle East" by the Council on Foreign Relations.
Since the start of anti-government protests last September, the Supreme Leader has relied on the IRGC to contain the popular discontent and maintain his tight grip on power. Reports indicate the Guards have opened fire on demonstrators and carried out summary executions, among other brutal tactics.
Over 520 people have been killed and nearly 20,000 have been arrested in Iran across four months of unrest, according to the US-based Human Rights Activists News Agency (HRANA).
As protesters and repressors continue clashing, a growing chorus of voices, led by the Iranian diaspora, demand the EU add the Revolutionary Guards to its official terrorist list, which currently includes 13 individuals and 21 entities, such as Hamas, the PKK and Hezbollah’s military wing.
But EU officials warn the legal basis is not yet solid enough: adding a new person or entity to the terrorist list requires a judicial decision by one of the bloc's member states. After that, the proposal is examined by a working party and then sent to foreign affairs ministers for approval, which needs unanimity.
"There are many interesting opinions about (the designation). But it is something that cannot be decided without a court – a court decision," Josep Borrell, the EU's foreign policy chief, said on Monday.
"You cannot say: 'I consider you a terrorist because I don’t like you.' It has to be when a court of one member states issues a legal statement, (and) concrete condemnation, and then we work at the European level. But it has to be first a court decision."
A European Commission spokesperson later told Euronews the legal ruling could also be issued by a "competent authority" in a "third country," that is a country that is not part of the European Union.
The spokesperson noted that the Revolutionary Guards, either as a group or as selected members, are already listed in the bloc's human rights regime and the sanctions in response to the Ukraine war, to which Iran has contributed by supplying kamikaze drones to Moscow.
So far, only the United States, Saudi Arabia and Bahrein have labelled the IRGC as a terrorist organisation, a move now under consideration in the United Kingdom and Australia.
The reticence in Brussels also stems from fears that slapping such a label on the Guards, which are technically a government agency, will definitely close the narrow window to revive the 2015 nuclear deal.
With the political debate gaining traction and supporters by the day, Iran has warned the bloc against moving forward with the designation.
"We have repeatedly said the Revolutionary Guards are a formal and sovereign organisation whose role is central for guaranteeing Iran's security," Iranian Foreign Affairs Minister Hossein Amirabdollahian told Josep Borrell in a phone call last week.
"Steps taken by the European Parliament to list the organisation as terrorist are in a way a shot in the foot of Europe itself."