By Agence France-Presse
The newspaper, quoting unnamed officials, said President Donald Trump's administration would announce the long-mulled decision as soon as Monday and that concerned defense officials were bracing for the impact.
The Islamic Revolutionary Guards Corp was formed after the 1979 Islamic revolution with a mission to defend the clerical regime, in contrast to more traditional military units that protect borders.
The Revolutionary Guards have amassed strong power within Iran, including with significant economic interests.
The Guards' prized unit is the Quds Force, named for the Arabic word for Jerusalem, which supports forces allied with Iran around the region including Syrian President Bashar al-Assad and Lebanon's Hezbollah.
The Trump administration has already imposed sweeping sanctions on Iran after withdrawing last year from an international agreement under which Tehran drastically scaled back its nuclear program.
A foreign terrorist designation would make any activities of the group toxic for the United States, with any transactions involving US institutions or individuals subject to punishment.
The Wall Street Journal said that the Pentagon and the CIA had reservations about the move, saying it would increase risks for US troops without doing much more to damage the Iranian economy.