The Government should also consider joint investment in the Whyalla wharf and other infrastructure, he said this morning in Adelaide.
Mr Shorten described Australia's steel industry as being "at a tipping point".
"There are measures which the Federal Government, Mr Turnbull, working with the SA Government and the Arrium company could put in place which will assist a sustainable future for steel manufacturing in this country," he said.
"Right now the steel industry's under attack.
"What we see is Chinese and Korean steel companies effectively engaging in the trade version of match fixing and we need the rules to back up our jobs and our people.
"So what I want to see is stronger anti-dumping laws."
More than 1,000 jobs are at risk if Arrium, the owner of the Whyalla steelworks, proceeds with a proposal to mothball it, which is a possibility if the company's financial situation does not improve.
Arrium this week recorded a half-year net loss of $236 million, with the Whyalla steelworks posting a $43 million loss.
Hundreds of jobs have already been axed at the plant.
Mr Shorten said Australia must continue to have a local steel industry.
"Other countries get that having a steel industry is important to national security," he said.
"Steel is a vital component of our warships, it's a vital component of our infrastructure.
"We would be mugs if we waved goodbye to the steel industry."
Local federal MP Rowan Ramsey told ABC North and West that it would be an unusual step for the Government to invest in Arrium but would not immediately rule it out.
"I would be pretty nervous about actually buying a share of the business, given the idea that somehow along the line the Government is going to run it more efficiently than private enterprise," he said.
"It's not the kind of experience that I've seen in the past."
He said the Government must do all it could to ensure the local steel industry survived.
"I think whatever gets suggested we can't just turn it back and say 'that's a dumb idea'.
"I think we need to talk about it and think about it.
"But co-investment is a pretty big jump for any Government."
Source: ABC.net