Mr Lees-Galloway refused to comment on his position, but it is understood he has been talking to other MPs about whether it was realistic to expect Mr Cunliffe to be able to stay on as leader.
He was one of Mr Cunliffe's staunchest supporters in last year's leadership contest, but is now expected to counsel Mr Cunliffe that it is best to step aside because he can not control caucus.
Another Cunliffe supporter, Su'a William Sio, is also believed to have expressed concern about Mr Cunliffe's ability to stay on but said today that was "inaccurate."
He said before the party's caucus meeting on Tuesday his Mangere electorate committee told him to back Mr Cunliffe in his bid to remain leader.
However, he would not say if he personally believed it was tenable for Mr Cunliffe to continue in the role following that caucus meeting.
"I'm not going to answer that question at all. I think I've made it clear the people of Mangere want to see him stay as leader. At the end of the day that's a decision DC needs to make after he considers all the comments made by the members of caucus."
It is understood at least three of Mr Cunliffe's supporters have broken ranks because of concerns he could not provide stable leadership even if he can secure a renewed mandate from the wider party.
Other Cunliffe supporters from last year's leadership contest did not return calls or refused to comment when asked if they believed he should stay in the role.
Carmel Sepuloni said she would not comment.
"I'm not going to talk about the leadership, anything to do with our caucus. I am looking forward to our caucus meeting next week when we can all go back after having reflected and having some time to think."
Nanaia Mahuta did not return calls today.
On Monday, she refused to comment on the leadership or say whether she supported Mr Cunliffe's bid for a renewed mandate as leader.
The bad election result meant Mr Cunliffe lost at least two other supporters in Carol Beaumont and Moana Mackey, who did not make it back on the list.
By Claire Trevett of the New Zealand Herald
