Labour leadership candidates have insisted they would not include Jeremy Corbyn in their shadow cabinets despite their rival's increasing support among party members.
Shadow minister Ms Kendall said the Opposition's top team would need to be "serious and credible", adding they would need to take on "very difficult issues" while also inspiring Labour supporters.
Aides to frontrunner Andy Burnham said he could not "envisage any circumstances" where Mr Corbyn would be on his frontbench, insisting the shadow health secretary was joking when he told a BBC debate he "might be open to listening".
In contrast, Mr Corbyn said Ms Kendall "would be there" in his shadow cabinet, telling BBC1's Sunday Politics: "I'm sure Liz and I could find some common ground on some issues somewhere. We may not have the same economic direction."
Fellow candidate Yvette Cooper said she did not want to "prejudge" the issue.
Mr Corbyn has defied his initial rank outsider status to replace Ed Miliband by securing the most nominations so far from constituency parties and reportedly topping some private opinion polls.
But asked if she would have Mr Corbyn in her shadow cabinet, Ms Kendall told Pienaar's Politics on BBC Radio 5 Live: "No."
Pressed to justify her stance, Ms Kendall said: "I believe you need to have a serious and credible shadow cabinet with people who are prepared to take on the very difficult issues we face as a party, as well as inspiring our supporters with a clear vision for the future.
"We've always been a broad church as a Labour Party but I think my politics comes from a very different place from Jeremy's and it wouldn't be right for him to be in my shadow cabinet."
Labour's Diane Abbott, who is a supporter of Mr Corbyn, said she did not believe the Islington North MP could win the leadership contest.
Asked if Mr Corbyn could win, she told BBC1's Andrew Marr Show: "No. These stories about where he comes first - no-one has seen such polls, that is a silly story.
"But he is doing very well and the reason Jeremy is doing very well is that the things Jeremy is talking about - peace abroad, social justice at home - are things that chime with Labour Party members.
"The sneering at Jeremy for believing in things that actually millions of people believe in - like we shouldn't be bombing Syria - and the attempt to abuse Labour Party members, we are hearing they are mad, that they are having a tantrum, that doesn't play well."
The endorsements for the leadership contenders also continued, with Ms Kendall receiving the backing of former Labour chancellor Alistair Darling.
Former foreign secretary Dame Margaret Beckett, one of 34 MPs who nominated Mr Corbyn, tipped Mr Burnham as the candidate most likely to win back power in 2020.
She said she is among those who lent their formal backing to left-wing stalwart Mr Corbyn to promote the widest possible debate but had never intended voting for him.
Dame Margaret, who led the party for a brief spell after the sudden death of John Smith, wrote in the Sunday Mirror: "I saw Tony Blair come from being an inexperienced shadow minister to someone who led Labour to victory. I am convinced Andy can build a movement to win again and change Britain for the better, to hold Cameron and Osborne to account and to win in 2020."
Ladbrokes said it had cut its odds on a Corbyn victory to just 10/3 - a far cry from the 100/1 offered at the start of the contest - making him the third favourite behind Mr Burnham at 10/11 and shadow home secretary Yvette Cooper at 11/4 but ahead of Liz Kendall out at 10/1.
The bookmaker said if the "relentless" backing continues, "it's only a matter of time before Corbyn moves into second spot in the betting".
Acting Labour leader Harriet Harman, plus the leader and deputy leader candidates have been warned the party could be "doomed to opposition" for a long period of time or even "on the road to extinction" if it fails to answer questions about its future direction.
Listening to Labour's Lost Labour Voters, by former senior Labour officials John Braggins and Alan Barnard, examined why previous Labour voters in five constituencies targeted by the party at the general election had not backed them.
In a letter, the pair say - among other things - Labour needs to establish what its purpose is, outline its reforms for the welfare state and explain how the party's economic credibility can be rebuilt.
They added: "The voters we spoke with told us that Labour doesn't have a God-given right to exist, and that there are plenty of parties out there now for them to choose from.
"They told us that Labour simply didn't speak to them ahead of the general election. They said that unless Labour makes itself relevant to their lives, they are prepared to stick with the Tories next time around."
The research project took place between May 21 and June 22, and involved discussions with voters in Tory-controlled Halesowen and Rowley Regis, Croydon Central, Southampton Itchen, Watford and Pudsey.