The officials stressed that no final decision has been made. The Obama administration is first asking the Syrian government "to take additional security measures."
But the administration apparently is prepared to pull out of Damascus if those conditions are not met. The State Department later put out a written statement saying that "unless concrete steps are taken in the coming days we may have no choice but to close the mission."
"While no decision has been made, we have serious concerns about the deteriorating security situation in Damascus, including the recent spate of car bombs, and about the safety and security of embassy personnel," the State Department said.
The department said Syria is "considering" the Obama administration's security request.
The move comes as the Obama administration continues to condemn the regime of Syrian President Bashar Assad for using violence against protesters in the country.
The uprising against Assad has killed an estimated 5,400 people since March. Although the revolt began with mostly peaceful protests, an increasingly strong armed element has developed, and many people are now fighting the regime.
The U.S. removed its ambassador to Syria, Robert Ford, from Damascus in October over security concerns. He returned to Syria in December.
The administration argued at the time that Ford's presence in Syria was important for advancing U.S. policy goals by meeting with opposition figures and serving as a witness to the ongoing violence.
The Obama administration has long called for Assad to step down, and officials say his regime's demise is inevitable.
U.S. officials say Syria has become increasingly isolated, with Iran as one of its last remaining allies, and point to recent defections by some military and government leaders as a sign that Assad's grip on power is unraveling. The 10-month uprising against Assad has turned increasingly militarized and chaotic as more frustrated regime opponents and army defectors arm themselves and fight back against government forces.
Fox News' Justin Fishel and The Associated Press contributed to this report.