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He said deputy leader Jacinda Ardern lack of appetite for the job ruled her out, while housing spokesman Phil Twyford would be "reasonably effective" but not a strong option.
Napier MP Stuart Nash was another name touted around. "He's a centrist politician, much more centre than Andrew would in any way resemble. If he could get support, he would certainly put up his hand."
Meanwhile, Soper said Grant Robertson, considered to be one of the more popular members of the Labour Party was unlikely to win over any more voters than Little.
However, Soper indicated it was more likely that come the end of the day Little would "bury" the question of leadership - one way or another.
Earlier, Little said he would not put a confidence vote on his leadership to the party's caucus this morning because he did not believe it was necessary despite a string of dire polls.
Last night a third poll had support for Labour in the low 20s in what has turned into Little's worst week in the job.
The Newshub Reid-Research poll had Labour on 24.1 per cent - the same as the One News Colmar Brunton poll on Sunday night and just above a result of 23 per cent in a UMR poll sent out last week.
That is perilously close to the 23 per cent Labour needs for Little himself to get back in Parliament on the list, if Labour holds all 27 of its electorate seats. If Labour wins more seats, the party would need more to get Little back in.
And it would mean other senior MPs, including David Parker and Trevor Mallard, would be out.
Little said he was not worried about being challenged at today's caucus meeting.
"I've got an honest and open relationship with caucus members and nobody has said that to me. In fact, they've said the opposite. So I'm not expecting it."
"All these polls were taken at roughly the same time. They're telling us the same thing about the same slice of time in which they were taken. What it tells us is what was a tough job has got tougher."
He admitted some MPs had told him that revealing he had raised the prospect of stepping down was "not helpful".
"I was being honest and I'm not going to apologise for being honest. I don't think anyone would think when I received a poll result like that I wouldn't talk to senior colleagues, and wouldn't say we've got to consider all valid options."
Little raised the prospect of standing down with senior colleagues last week and said he had forewarned all MPs about the polls last Friday.
Those colleagues included deputy leader Jacinda Ardern who said yesterday she backed Little to stay in the job.
Labour's rules usually require a full vote of party members, MPs and union affiliates but in the three months prior to an election, the caucus can elect a new leader by a majority vote.
Some MPs were publicly backing Little yesterday, including Stuart Nash who said if there was a change in leader this close to the election "we would be doomed".
"Of course people are concerned about the result, you'd be lying if you weren't. But he has my support 100 per cent.
"I think a change in leader would doom us. Absolutely doom us. In fact, it could put the party itself in jeopardy."
Frontbencher Phil Twyford gave a less ringing endorsement: "I support the leader of the Labour Party as long as he is the leader of the Labour Party."
He said nobody was satisfied with the poll numbers.
"But the responsibility to deliver messages and explain our policies is not just Andrew's. It falls on all of us so it is a collective responsibility."
The 24.1 per cent Reid Research result was Labour's worst result in the poll's nine-year history. The main beneficiary appears to have been NZ First, which was up almost 4 points to 13 per cent.
That contrasts with the Colmar Brunton poll which showed a boost for the Green Party while NZ First stayed steady.
The Reid Research poll also had National down 2.2 per cent at 45.2 per cent - meaning National would need NZ First to form a government.
And National was also busy trying to ensure its voters did not get complacent. Prime Minister Bill English said National had to hold its own vote up to be sure of getting back into Government.
Last night, an email from Minister Judith Collins also went out to supporters with the subject heading: "they can still win."
It read: "The opposition is bitterly divided but under MMP the polls show they can still win. All of our economic strength, growth and security will be at risk, and because they're so divided we don't even know who they'd have as Prime Minister.
"I am urging you - please do not be complacent, National needs your Party Vote."
The Reid Research poll also showed Little's deputy Jacinda Ardern had climbed further as preferred Prime Minister.
That poll has Ardern up almost two points to 8.7 per cent as preferred Prime Minister, while Little was on 7.1 per cent. National leader Bill English was on 25.8 per cent and NZ First leader Winston Peters on 11.9 per cent - up 2.2 points since the last poll.
Ardern is considered the most likely to replace Little if he goes either before or after the election.
The Newshub Reid Research poll of 1000 voters was taken from July 20 - 28 and included 750 respondents by telephone and 250 by internet panel. It has a margin of error of +/- 3.1 per cent.
