Risk factors would include families on the benefit, siblings who have been victims of abuse and parents who have been in prison.
Ms Parata said no desicion had been made yet on improving the funding system.
"As well documented, any changes to the funding system won't be in place till 2020," she said.
John Paul College principal Patrick Walsh described the current decile system as a "blunt instrument for assessing deprivation and achievement".
But he said schools would have to be bold enough to give the replacement system a go.
"We have to just go for it and hope for it to be an organic process that we can work on and respond to," he said.
"I want to see a system which offers support for our at-risk students."
John Paul College is a decile 7 school.
"I think people think high decile schools are awash with money, or that our children all come from high income families, and that just isn't true," he said.
"Students should be able to be assessed individually."
Mr Walsh said he wouldn't want the new system to take away from lower decile schools.
"No matter how much we cut across the resourcing pie, there still isn't enough pie to go around," he said.
Otonga Primary School is also decile 7. Its principal Linda Woon agreed schools were "chronically underfunded".
"I see what she [Ms Parata] is trying to do, and I appreciate that she's trying to do something, however year by year the funding levels drop in many ways," she said.
"I'm not going to judge before I've seen the new system, but it does leave us feeling a little insecure when we're already chronically underfunded across the board."
Sunset Primary School is a decile 1 school.
"There's a stigma attached to our students, and the changes would only further encourage that being attached to students," principal Niels Rasmussen said.
"That's always going to be an issue when you're ranking schools and deciding who's entitled to what."
Mr Rasmussen said the school could handle people's perception of them.
"No schools get enough funding, but that's only the tip of the iceberg," he said.
The current system - the decile system
The decile system came into existence in 2008.
Deciles are a measure of the socio-economic position of a schools student community.
School funding is based on the decile ranking, 1-10.
The decile system does not reflect the quality of education the school provides.
Deciles are recalculated every five years.
During the 2014 recalculation, 800 schools moved to a lower decile and had their funding increased, while 784 schools moved to a higher decile and saw their funding reduced. The rest remained at the same level.
The proposed system - the predictive risk index
Will measure the number of individual students who are at risk, as assessed by government data.
Factors that may identify students as at risk are from families on a benefit, with brother and sisters who have been victims of abuse, or parents that have been in prison.
School funding will be based on the number of students it has with risk factors.
The predictive risk index system will not reflect the quality of education the school provides.