The Metropolitan Police have made knife crime their top priority
Hospitals could be asked to release figures on people treated for stab wounds in order to gauge the true extent of knife crime.
Home Office minister Tony McNulty said discussions with health ministers were taking place. He also warned carrying knives was "in youngsters' DNA".
Currently gunshot wounds are reported to police but stab wounds are not.
An Independent on Sunday investigation suggested that almost 14,000 people a year are injured in knife attacks.
Policing minister Mr McNulty told the Adam Boulton show on Sky News: "I know again there is a balance between an individual's privacy in terms of turning up at a casualty and the national health system providing those figures so that we all know the full extent of knife injuries.
"And I think there really should be a debate about that and one that I am trying to pursue with my health colleagues."
Last week Metropolitan Police Commissioner Sir Ian Blair vowed to step up police efforts to reduce knife crime, following the death of 16-year-old Ben Kinsella, who was the 17th teenager this year to be killed in London.
Since then, another teenager, 16-year-old Shakilus Townsend, died after being beaten and stabbed in south London. The force has since said tackling knife crime is its "number one priority".
Mr McNulty said the "recent tragedies" were "appalling" but the problem could not be solved by the government alone.
"I'm afraid this is apparently a generational, almost cultural thing that's getting into the collective DNA," he said.
"It's not a cop out to say this is something that goes to the heart of our entire society."
He added: "It is about, classically, the causes of crime as well as crime."
He called on judges and magistrates to use powers to impose tougher sentences on people caught carrying knives.
And he said youngsters had to be sent a message: "If you carry a knife, you either use it, it's used against you, and potentially you either end up dead or in prison. And it is as stark as that."