"We are currently considering two options for our future embassy facility in Jerusalem," Price said during a press briefing.
"One is the Allenby site and the second is the Arnona site. But, again, no decision has been made on site selection."
The United States has started the process to amend the Jerusalem town plan for both potential locations in accordance with Israeli legal requirements, Price said.
The current US embassy is located in a temporary building in the Arnona neighborhood.
US Secretary of State Antony Blinken announced in May that the US is also planning to reopen its Jerusalem consulate exclusive to the Palestinian territories.
The US consulate had been operating in East Jerusalem for decades, being the country's de facto diplomatic mission for the Palestinians. Under the presidency of Donald Trump, it was merged with the US Embassy in Israel in 2018, which was moved to Jerusalem from Tel Aviv.
The United States recognizes Jerusalem as Israel’s capital while the status of the city remains contested by the Israelis and the Palestinians.