This week it emerged that Labour had objected to TVNZ's choice of its Seven Sharp presenter Mr Hosking as its election debate moderator because of pro-National comments he had made, including while acting as MC for Mr Key's 2013 State of the Nation address in 2013.
Mr Cunliffe said Hosking's apparent endorsement of National "raised some questions that TVNZ will want to very carefully consider."
Mr Key had challenged Mr Cunliffe to a debate on housing affordability at his weekly post-Cabinet press conference in April, saying:
"If David Cunliffe wants to have a bit of a chat on nationwide TV about it, I'm more than happy to do so. We'll call it the first debate. I'm looking forward to it."
Mr Cunliffe said he would gladly accept any such invitation. "I can't think of a more important topic to be debated publicly, and I think it's my obligation as leader of the Opposition to rise to that challenge."