If confirmed, Lakhdar Brahimi would succeed former UN Secretary General Kofi Annan, who resigned last week saying he could no longer carry out the role.
A six-point peace plan proposed by Kofi Annan failed to come into effect, and violence has escalated.
Rebels lost control of a key area of Aleppo after weeks of fighting.
The rebel Free Syrian Army (FSA) confirmed it had retreated from the strategic Salah al-Din district in the face of a large-scale government offensive launched the previous day.
Lakhdar Brahimi’s appointment could be announced as early as next week, barring last-minute objections from governments, diplomatic sources told journalists.
Lakhdar Brahimi, 78, has held a long series of high-profile diplomatic posts.
As a senior Arab League official between 1984-91, he brokered an end to the Lebanese civil war, going on to serve as Algerian foreign minister between 1991-3.
Later, he was twice appointed as the UN’s top envoy for Afghanistan, in 1996-8 and in 2001-4. He has held similar roles for Haiti and South Africa.
Stepping down last week, Kofi Annan said he was unable to fulfill his role because of the growing militarization of the conflict in Syria, as well as the continuing deadlock over the issue in the UN Security Council.
Russia and China have vetoed resolutions on the crisis three times, citing their opposition to any action which might be seen as regime change imposed from outside.
After taking up his post in February, Kofi Annan formulated a peace plan that called for an end to the use of heavy weaponry, the free passage of aid, freedom of media and demonstration and for a Syrian-led political process to address the aspirations and concerns of the Syrian people.
It was supposed to come into effect in mid-April, but government forces continued to shell opposition strongholds and the opposition forces never fully committed to it.
The fighting recently intensified in the two main cities, with experts describing it as a new phase in the conflict.
Rebel fighters had been heavily embedded in Aleppo’s Salah al-Din district since seizing the densely packed area of narrow streets three weeks ago.
The rebels still control several other districts, including some in the east of Aleppo that activists said came under very heavy bombardment on Thursday.
State television said dozens of rebels had been killed or wounded in fighting in the Hananu quarter.
Aleppo is Syria’s largest city, and Salah al-Din is considered a vital supply route for government troops coming from the south.
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