It's an idea Justice Minister Peter MacKay has said the federal government is actively examining.
Alberta Premier Alison Redford and Calgary police Chief Rick Hanson support the concept too.
But many are uncomfortable with the idea of holding the genetic material of people who might never be charged, let alone found guilty.
Speaking on CBC-Radio, Paulson said he's in favour of taking samples from people when they're arrested.
"The Identification of Criminals Act has been very well tested and has endured for fingerprints and so on. And I think that the more DNA we can get, the better we're going to be," Paulson said.
Privacy vs. protection of public
Canada's DNA databank contains the blood, saliva and hair of roughly 266,000 people who have been convicted of a crime.
The U.S. Supreme Court ruled this year that police may swab people on arrest.
Bernard Dickens, a professor emeritus at the University of Toronto, said the split decision in the American court illustrated the debate over giving police more investigative powers.
"The narrowness of the 5-4 decision shows that the contrast between preservation of individual privacy and protection of the public so that wrongdoers are identified can be a very narrow balance," Dickens said.
In Canada, the opposition parties aren't on board with the idea.
Liberal MP Wayne Easter used to be Canada's solicitor general.
"It's a person's genetic footprint. [It] tells you a lot more information than just the identity of the person ... there's a whole range of privacy issues," he said.
NDP public safety critic Randall Garrison said seizing DNA before someone is charged — let alone found guilty — would not respect an important principle of the criminal justice system.
"We do still have the presumption of innocence in this country and so I would have very serious concerns about DNA sampling upon arrest rather than at conviction."
Garrison added an expanded database would cost a fortune.
The RCMP runs the national DNA database. Paulson conceded it might be tough to process, manage and store so many new samples.
"It'll be an administrative, logistical challenge, but I think we'd be up to it," he said.
Concerns about profiling
Dickens raised concerns about profiling.
"The danger is of the police being able to act without discipline of justifying what they propose to do to the independent scrutiny of a judge," he said.
But Michael Kempa, a criminologist at the University of Ottawa, said seizing DNA on arrest is part of the criminal justice continuum where law enforcement is trying to be pre-emptive and manage risks as well as people it feels are risky.
"It's just the state doing more of what they've always done because they're able to. So if all we have are ink and paper and we can take fingerprints, we'll do that. But as we evolve this technology we can find out [and] store more and more about you and your DNA," said Kempa.
He added it would be up to society as a whole to debate and decide the legal limits on how the information could be used and how much profiling should be tolerated.
So far the government has not moved to change the DNA Collection Act, but experts predict any such legislation would kick off a constitutional challenge.