Urgent efforts are under way to find a replacement for the UN's special envoy on Syria, Lakhdar Brahimi, who is expected to resign his post by the end of this month.

After the failure of the Geneva peace talks and President Bashar al-Assad's confident decision to stand for re-election, Kevin Rudd, the former Australian Labour prime minister, and Michael Williams, a British veteran of the UN and now a peer, have emerged as leading candidates for the most important – and probably the most thankless – role in world diplomacy, which is in effect paralysed in the fourth bloody year of the Syrian crisis.

Diplomatic sources confirmed on Thursday that the other names on the UN shortlist are Kamel Morjane, a former Tunisian foreign minister, and Javier Solana, the Spanish politician who has been both Nato secretary general and the European Union's foreign policy supremo.

Brahimi is due at the UN in New York on Friday and is expected to brief the security council on 13 May. But the Guardian understands that it is almost certain to be his final appearance.

The veteran Algerian mediator, who is 80, has been in the job since September 2012, when he replaced Kofi Annan, the former UN secretary general. Brahimi had threatened to resign almost from the start of his mission but officials at the UN and elsewhere insisted that this time he meant it.

Annan and Brahimi both represented the UN and the Arab League – as "joint special representative" – but the new appointee is expected to report only to the UN because of the deep divisions within the Arab world over Syria.

Saudi Arabia, Qatar and other Gulf states openly back the anti-Assad rebels, while countries such as Algeria and Iraq stand solidly behind Damascus. "The Arab League's role has become a drag because of the divisions," said one well-placed source. "It's not an asset but a hindrance."

Britain, one of the five permanent members of the UN security council, faces a tough choice. Rudd is admired by David Cameron and the foreign secretary, William Hague. The Australian, a former diplomat, is said to have his eye on becoming secretary general of the UN – though the next incumbent, according to the principle of continental rotation, is expected to be a European.

The Syria envoy position could be seen as a stepping stone to that, though success is clearly not guaranteed in a job some have described as a poisoned chalice. Rudd has a reputation in Australian politics for being abrasive.

Rudd's public calls for Assad's departure when he was foreign minister in 2011 may also count against him.

Lord Williams has a lower profile but the advantage of extensive experience in the UN. The former BBC journalist has served in Cambodia, the former Yugoslavia and has rich regional experience as the UN co-ordinator for the Middle East peace process and its representative in Lebanon.He also served as Middle East adviser to Gordon Brown in Downing Street. Friends say he would see the Syria role as a moral obligation, despite its obvious difficulty.

Morjane's candidacy is important because for political reasons an Arab name must be on the shortlist, though the Tunisian government is reportedly unenthusiastic about it. Spain's Solana is seen as the least likely of the four to get the job.

Brahimi presided over two rounds of peace talks between the Assad government and opposition representatives in Geneva in January and February but they yielded no results except for a week-long ceasefire in the partially besieged city of Homs. Brahimi's deputy in Damascus, Mokhtar Lamani, quit in March.

The decision on Brahimi's replacement will be taken by Ban Ki-moon, the UN secretary-general, but he is expected to consult security council members as well as Germany and Turkey.

Diplomats working on Syria admit privately that they feel overwhelmed by the magnitude of the crisis, the despair about making any progress and the new complications caused by rising tensions between Russia and the west over Ukraine.

According to the latest figures more than 150,000 people have been killed since the anti-Assad uprising began in March 2011 with peaceful protests against the background of the Arab spring. But Syria is now embroiled in a fully fledged war that has drawn in foreign forces and support on both sides. Up to 2.5 million people have fled abroad and 9 million people inside Syria need help in what the UN has described as the world's worst humanitarian crisis in modern times.

Meanwhile, Syrian opposition activists say at least 33 people were killed in a government air strike that targeted a busy street in the northern city of Aleppo on Thursday. The air strike on the Hillok district of the rebel-held eastern part of the city also injured dozens of people.