But SA Premier Jay Weatherill has been swift to hose down the suggestion.
The Budget and Finance Committee has heard SA Police must find $150 million of savings over the next four years.
Mr Burns concedes it will be hard to find those savings and says cuts to police numbers will have to be looked at.
"Our aim will always be to make sure that we're delivering the best front-line services we can and to move people into the front-line where we can," he told the committee.
"The last thing we want to do is to reduce police numbers, but it's on the cards that we'll actually have to look at our workforce."
Mr Burns said the force might try to save money when officers resign or retire by delaying recruitment of new police.
He said 77 per cent of the police budget went on salaries.
Mr Weatherill said there would be no cuts to police numbers in South Australia and no impact on front-line services.
"There'll be no cut in police, in fact police numbers will grow," he said.
Police Association president Mark Carroll said he would meet the Commissioner on Tuesday to discuss budget cuts.
He said it was hard to see how the savings would be made.
"Almost 80 per cent of the police budget is made up of wages. There are other fixed costs that take up another 10 per cent of the police budget, [so] we're talking about uniforms and cars and vehicles and of that nature, so there's not too much fat left on the bone," he said.
"We know that policing by its very nature is labour intensive. We know that law and order is the cornerstone of a free and democratic and prosperous community so we want, people want to see more police, not less of them."
A review of the Adelaide Women's and Children's Hospital is to be done by consultancy firm Deloitte as the South Australian Government looks for savings.
SA Health CEO David Swan said it follows hospital budget and performance reviews done last year across the metropolitan local health networks.
"The three reviews, completed by KPMG and Deloitte in July 2012, resulted in a range of significant savings and efficiencies being implemented across the Central, Northern and Southern [networks]," Mr Swan said.
He said there would be consultation with staff across the range of hospital services and the review was expected to be completed by May.
"We want to make sure that all of our services and operations are operating as efficiently as possible. We want to make sure they're delivering very efficient services to the public," he said.
Previous reviews recommended jobs be cut in the health sector.
Family First MP Rob Brokenshire said Parliament should have to approve any increase in the South Australian Government's net debt above $14 billion.
Mr Brokenshire urged legislation be amended to help protect the state's economic future by holding the Government accountable.
"They can just rack that debt up providing they can get a financier to give them the money," he said.
"Now that's simply not satisfactory and, having worked through this before, I am so frustrated as indeed are South Australians generally that I believe we must now have a check and balance on the Government of the day.
"Frankly, we can't afford the debt we've got now. We're in a very, very precarious financial position and I think it's time that there was pressure put on Government to stop them racking up debt at the expense of our future generations."