In recent weeks, Assad has disappeared from the public eye, giving no interviews or speeches and making no "live" appearances on state-run television, The Washington Post reported.
"His movements suggest a constant state of fear," a Middle Eastern official said on the condition of anonymity.
Assad has previously stated he will not concede the presidency. In November, he vowed to "live in Syria and die in Syria."
"Assad may still believe Syria is his, but the psychological strain of struggling against a determined and resourceful foe has to be taking its toll," said a U.S. official, who spoke on condition of anonymity.
A senior U.S. official said that although defections -- most recently the chief of the Syrian military police -- have likely shaken Assad, he still has a core group of loyalists.
"Assad's levers of influence are fraying and his reach is contracting, but the regime core is a tough nut that doesn't seem to be cracking just yet," the senior U.S. official said. "Although pressure is mounting, it's difficult to say when the breaking point will come because there's little to suggest that Assad is a cut-and-run kind of guy."
Syria has been embroiled in a civil war for going on 22 months. Since the beginning of the conflict, 44,000 people have died inside the country.
Saturday, the Syrian Network for Human Rights said 226 people were killed across Syria, including 29 children and 24 women. The figures were not independently confirmed.