The strike, which began last week, has led to the closure of schools across 110 districts.
The teachers' original demands included competitive pay for teachers and support staff, annual raises, a restoration of education funding to 2008 levels, and no new tax cuts until per-pupil funding reaches the national average.
The legislature is expected to vote Wednesday as walkouts are expected to continue that day.More news: Investigators have floated idea of subpoena for Trump
The deal would increase teachers' pay 20 percent by 2020 and provide an extra $371 million in school funding over five years.
"We have delivered a win in this session", Arizona Educators United organizer Noah Karvelis said. "But it is time for us to get back to our students and get back into our classrooms". Then he came up with a new spending plan.
Arizona teachers are slated to end up back in their classrooms by Thursday if the budget as written is passed.
"We have so many people now that are paying attention to what's going on, they will never turn away from this fight now", he said.More news: Congress politics blocked development in Karnataka, says Modi
But Ducey said in a letter to teachers released to the public on Tuesday that he and lawmakers were 'very close to passing a significant budget investment into K-12 education'.
Arizona Education Association President Joe Thomas said the plan is to go back to work while looking ahead at what options at the ballot box are available to make changes in state education funding. "They understand that there are people down here who do not care as much about students as they care". Some districts are expected to stay closed Wednesday.
Arizona teachers say they will rally for one last day at the state Capitol for before ending their historic walkout for education funding. Teachers also organized food drives for students who rely on free and reduced lunch.
Many community members supported teachers' efforts, but pressure was increasing on some parents and school administrators.More news: Alleged Sexual Predators Don't Need Letters Of Support
But Trujillo was concerned teachers would lose public support if the strike dragged on. "Now that we're into day four, I think that's on the line".