The State Department in March ordered the Libyan Embassy closed and told members of the regime of Libyan leader Moammar Gadhafi to leave the country.
NATO-led forces in March started enforcement of a U.N.-mandated no-fly zone over Libya as part of an effort to protect civilians from attacks by Gadhafi's military.
The rebel-backed Transitional National Council had asked Washington for permission to reopen the embassy under its authority, asking that Ali Aujali represent the country as the Libyan envoy to the United States.
A source in the State Department told CNN on condition of anonymity that Aujali could become the next ambassador after he settles his diplomatic status. He resigned as the Libyan envoy to the United States in February and later supported the rebel leadership.
London recently followed suit as other European governments voice support for the TNC.
Chris Stevens, the U.S. representative to the TNC, said that despite a lengthy military stalemate in Libya, the rebel leadership was making "tremendous progress" on the diplomatic front.
Reindeer recovered after escaping from Santa during lighting ceremony
Wisconsin business offering 'therapeutic cuddling' forced to close