While the rebels have yet to seize a major airport, they have disrupted traffic at some with heavy machine-gun fire, and flights to Damascus have been canceled due to fighting near its airport.
Syrian airlines is the only carrier still flying to Damascus, running one flight per day, though some officials still consider the trip too risky.
Last week, Brahimi flew into Beirut and drove to Damascus overland to avoid the airport. On Saturday, Lebanese security officials said Syrian Deputy Foreign Minister Faisal Mekdad did the same while returning from Moscow.
The officials spoke on condition of anonymity because they were not authorized to brief the media.
Aleppo's international airport is just southeast of the city and still controlled by the government. It sits next to the Nerab military airport. The base of the army's 80th Brigade is nearby.
Rebels have been clashing with government troops near the airport for days, and videos posted online show them firing homemade rockets and shooting at targets inside. The videos appeared genuine and corresponded to other reporting by The Associated Press.
An Aleppo activist said the area's rebels see the airport's capture as a clear way to weaken regime forces fighting in the city since it is used to bring in supplies.
"Since the rebels have targeted all the supply roads, the airport is the main way for forces in the city to get supplies, so if they can take it over it will be a big blow to the regime," the activist said via Skype, speaking on condition of anonymity out of security concerns.
He and other activists reported a large explosion inside the airport on Friday, though it was unclear what caused it.
Illustrating the danger of the government's air power, anti-regime activists reported a number of deadly airstrikes in different parts of Syria, including in the towns of Azaz and Tel Rifat north of Aleppo and al-Nishabiyeh, south of Damascus.
Rebels also clashed Friday with soldiers inside the Mannagh helicopter base near the Turkish border.
Anti-regime activists say more than 40,000 people have been killed since the start of Syria's crisis in March 2011.
Associated Press writers Maamoun Youssef in Cairo and Vladimir Isachenkov in Moscow contributed reporting.