A National MP says there is a "huge mood for change in the backbench" and "Bill English shouldn't just be anointed".
In the strongest sign yet of disagreement in National's ranks about the next leader, the MP spoke under condition of anonymity to Newshub's political editor Patrick Gower.
The MP said "contenders" would emerge after Tuesday's caucus meeting.
"There's been one way of management for 10 years. Now is the opportunity for change," the MP said.
The MP declined to comment on whether this meant there was backing for a bid by Judith Collins, or just a contest for the job.
Bay of Plenty MP Todd Muller joined the chorus for change, saying there was "probably an appetite for a contest".
"We're reflecting on the national party direction for the next three years and possibly beyond."
He says a competition will allow the rest of the caucus to "get a sense of where people intend to take the party over the next three years".
Prime Minister John Key responded to the claim, saying that view is inevitable.
"There'll always be a view that people will take, but you could also say there's been one way of managing things for the last 10 years - it's been me a Bill - and it's been a pretty successful 10 years."
He said a competition would be healthy.
"If people want to put their name forward, they'll put their name forward.
"I've put my cards on the table when it comes to the leadership, but in the end it is up to others."