Premier Ben Carroll wants the royal commission into criminality and corruption on Victoria’s Big Build to start before November’s state election, and says he would appear as a witness if called.

Speaking at the Northern Hospital in Epping on Sunday morning, he said he had commissioned the head of the Department of Premier and Cabinet to consult on the terms of reference.

“This will be a completely independent process,” he said. “I’m not waiting for the report. I’m setting up a special prosecutor to work alongside the royal commission to get on with doing what they need to do straight away.

“This is not something that can wait. This is something that needs to be done now.”

Last week, after deposing Jacinta Allan as premier, Carroll confirmed the royal commission would examine previous Labor governments’ oversight of corruption on state government building sites. Integrity experts say the commission should examine the influence of donations and the relationship between the CFMEU and the state government.

On whether former premier Daniel Andrews and Allan would be questioned, he said the royal commissioner should question everyone they believed had a role.

“That will be a matter for the commissioner and the terms of reference,” Carroll said. “They will be wide and they will be exhaustive.”

Carroll said he would consult the cabinet this week before making a statement next week on the royal commission terms of reference.

Opposition Leader Jess Wilson released her proposed terms of reference for a royal commission on Saturday, with Andrews, Allan and Carroll among those suggested for the witness list.

Carroll said his office was still hunting down Wilson’s list.

“We haven’t been able to find it,” he said. “I think the media got a copy of it before I did, and I’ve asked my office to collect out a copy.”

Carroll did not indicate who would take up his portfolio of education in his forthcoming cabinet reshuffle, earmarked for this week.

The portfolio is under pressure from continued teacher strikes over a stalled pay deal.

“It’s a very good portfolio, and I think it’s one of the most important portfolios in government,” he said. “You get to change lives, and I’m very proud of the investments and reforms I’ve made, and I’ll always be having a very close eye on it.”

The Australian Education Union met on Friday and voted for a 24-hour strike on August 19, the third strike in the year-long negotiations in a bid to secure a better pay deal and conditions.

Union members rejected the Allan government’s July offer, which included a 28.3 per cent pay rise for teachers and education support employees.

Carroll said he was taking advice on whether he would go to the Fair Work Commission to halt the protest and would “use every resource we can”.

He said he had not met union officials to resolve the dispute since becoming premier last week after an internal revolt led to Allan stepping down.

“I’ve always wanted to work constructively with the union,” he said. “My door is always open. We are talking with the union from a departmental perspective. It was a very close vote last time, and I’m sure we can get there.”

Carroll urged teachers not to strike next week, as the union’s left faction plans to start smaller sub-branch actions from Tuesday, August 4.

Spokesperson Lucy Honan said at a strike committee meeting on Friday that the group resolved that August 19 was too far away, and they wanted to build towards the state-wide stop work.

“It will be disruptive but at a local level,” she said.

Actions are expected in the peninsula region, Fitzroy, Preston, Geelong and Footscray area and could range from cancelled classes, leafleting malls, and actions before and after school and during lunchtimes.

Honan said it would be formalised this week and parents would be notified. Any stop work or cancelled classes were more likely to be at the end of this week or next week, she said.