"We're looking into it along with a range of other proposals to impose further costs on Russia," Jean-Pierre said during a briefing on Friday.
Jean-Pierre noted that the US government has already imposed measures against Russia whose consequences equal those the SST designation would exact on the country.
"The cost that we have imposed are in line with some of the consequences of an SST designation," she said. "Russia defaulted for the first time in more than a century."
The comments come amid heightened tensions between Moscow and Washington after US House Speaker Nancy Pelosi reportedly urged Secretary of State Anthony Blinken to designate Russia as a state sponsor of terrorism.
On Thursday, the US Senate unanimously approved a non-biding resolution asking the State Department to apply the SST designation on Russia.
The United States has so far designated Cuba, North Korea, Iran and Syria as states sponsoring terrorism.