According to the WSJ, the move could be an operational and legal challenge for the company that could set a precedent for other tech giants.
The preliminary order, the people said, was sent by Ireland's Data Protection Commission to Facebook late last month, asking for the company's response.
It is the first significant step EU regulators have taken to enforce a July ruling about data transfers from the bloc's top court. That ruling restricted how companies like Facebook can send personal information about Europeans to US soil, because it found that Europeans have no effective way to challenge American government surveillance.
To comply with Ireland's preliminary order, Facebook would likely have to re-engineer its service to silo off most data it collects from European users, or stop serving them entirely, at least temporarily.
If it fails to comply with an order, Ireland's data commission has the power to fine Facebook up to four percent of its annual revenue, or $2.8 billion.
Nick Clegg, Facebook's top policy and communications executive, confirmed that Ireland's privacy regulator has suggested, as part of an inquiry, that Facebook can no longer in practice conduct EU-U.S. data transfers using a widely used type of contract.
"A lack of safe, secure and legal international data transfers would damage the economy and prevent the emergence of data-driven businesses from the EU, just as we seek a recovery from COVID-19", Clegg said.