At the same time, Soper says there's a feeling he should leave on his own terms and with dignity.
So far National MPs are publicly denying a leadership coup is afoot.
Invercargill MP Sarah Dowie conceded there has been "some talk", but insisted the caucus was united.
"Everyone is behind Bill, everyone is behind [deputy leader] Paula [Bennett], we're just focused on policy," she said today.
Questioned by media this morning, Auckland Central MP Nikki Kaye - whose name has been circulated as a potential candidate for the leadership - ruled herself out of standing for leadership and expressed full confidence in English and Bennett.
Senior MP Gerry Brownlee said "of course" when asked if he backed English.
Tim MacIndoe said he had "absolute faith" in National's leadership team.
New Tukituki MP Lawrence Yule said had not heard any talk of a leadership change and he believed the leadership team was secure.
Bennett has responded to speculation that her position might be in question, saying she has no intention of stepping down and she does not expect a challenge.
"We are a strong opposition who are focused on holding the Government to account," she told the Herald this morning.
Asked if she was considering stepping down, she said: "Of course not."
Her comments follow speculation this morning that her position as deputy leader may be uncertain, and that there are rumblings within the caucus about the leadership team.
"I'm focused on leading National back into government and I happen to be giving a speech today outlining how we are going to do that, including the party's focus for the year ahead and how we will hold this Government to account," English said in the statement this morning.
Senior MP Steven Joyce dismissed the speculation.
"Bill English is the leader and actually he has the support of the whole caucus," Joyce told Newstalk ZB this morning.
"This is classic first day journalists who will speculate on National Party leadership, job done. Typewriter down."
Joyce said English proved himself by getting the highest party vote at last year's election and that the first polls of the year will show National still ahead of Labour.
"That's one of the reasons why he won't be going anywhere. He is leading us well, and as we know he got the highest vote in the last election and everybody supports him."
Asked if Paula Bennett was going to get rolled, he said "No."
He believed the leadership team was not going to change for the rest of the year, unless English decided to step down.
"Bill English is in charge and unless he decided to do something at some point, that's the way it will continue."
Joyce said the caucus meeting in Tauranga next week had nothing to do with a possible leadership change.
"It is to discuss policy and our plans for the year ahead. Being in Opposition, we've got the opportunity to go out from Wellington to do it."
