Labour leader Andrew Little has said he would rather have an early general election than a byelection.
He said that following Key's resignation, the chances of the new Prime Minister holding an early general election, are likely.
"We have anticipated that there could be an earlier election and more so given the change of leadership in the National Party.
"So I think I'd probably rather avoid a byelection and just get straight into an earlier election."
Little said no thought had been given to who should run in the Mt Albert seat for Labour in place of Shearer, but people would be queuing up.
Byelections are costly - about $1 million according to the Electoral Commission - and have low voter turnout.
In the last one, for the Mt Roskill seat after Phil Goff stepped down and became the Mayor of Auckland, the voter turnout was just 16,857 (38.5 per cent) of the 46,133 enrolled before election day.
Labour MP Michael Wood won the seat with 11,170 votes, followed by National's Parmjeet Parmar with 4652 votes.
The only other byelection in the past two years was in Northland when Mike Sabin resigned.
New Zealand First leader Winston Peters won with 16,089 votes, followed by National's Mark Osborne with 11,648 votes.
Voter turnout was 65.4 per cent (30,047) of the 45,955 people enrolled.
Little said he heard from Shearer two weeks ago that he had been offered the role at the UN and that he wanted to accept it.
"We are very excited for him," said Little.
"Should he be confirmed, David will be the only New Zealander in charge of a UN peacekeeping mission. This is a very exciting opportunity for him to make a difference and help bring peace to a country of nine million people torn apart by civil war.
"We fully understand his reasons. This is a once-in-a-lifetime opportunity to take up a senior position at the United Nations which reports directly to the Secretary-General."
Shearer said this morning the Security Council would be making a decision on his post.
"There has been a high degree of media interest in New Zealand about a possible post with the United Nations," he said.
"My name has been proposed to the United Nations Secretary-General to be his special representative in South Sudan.
"The matter is before the Security Council for its decision.
"Until the Council completes its consideration of the appointment I will not be commenting further."
Little said the Special Representative and head of the United Nations Mission in South Sudan (Unmiss), is regarded as "the most challenging of peacekeeping operations currently".
Unmiss is the UN's third-largest peacekeeping mission with 17,000 uniformed and almost 2000 civilian personnel. It is charged with building peace and stability in what is the youngest country in the world.
The appointment is a personal one by the UN Secretary-General. It does not require a nomination by the Government.
But Foreign Affairs Minister Murray McCully said Shearer, who is Labour's foreign affairs spokesman, had the strong support of the Government.
"It is a huge deal," he said.
"[Security Council members have] a couple of days to raise any concerns, so it is not a done deal yet.
"But it is a big feather in his cap.
"This is the toughest peace-keeping assignment on the planet. It is a difficult and dangerous place."
