The Government and the Intellectual Property Office (UK-IPO) are consulting on the plans, which would allow Magistrates' Courts in England and Wales to issue summary fines of £50,000 for online copyright infringement.
The larger fine is proposed for commercial scale infringements, where the person involved profits from the infringement.
The plan would implement another of the recommendations of the Gowers Review of Intellectual Property, the 2006 report by former Financial Times editor Andrew Gowers which has been the foundation of intellectual property policy since its publication.
"This consultation takes forward Gowers Review recommendation 36, which recommended matching penalties for online and physical copyright infringement by increasing sanctions for online infringements," said the UK-IPO in a statement.
A report called 'Creative Britain' published by the Government's business, culture and innovation departments earlier this year also called for an increase in the maximum fines available to Magistrates Courts for online copyright infringement.
Gowers said in his report that online commercial infringement could not be as severely punished as commercial infringement in the offline world.
"Several submissions have called for a change in the law to increase online infringement penalties to the levels of physical infringement," he said in his report. "The intention and impact of physical and online infringement are the same. Crimes committed in the online and physical world should not be subject to different sentences. Increasing the penalties for online infringement will therefore make the law more coherent."
The UK-IPO said in its consultation paper that the change in the fines available to courts would allow them to better combat commercial scale infringement.
"Our investigations concluded that introducing exceptional summary maxima fines would allow magistrates’ courts to deal effectively with copyright offences as they would be able to award fines that took account of the illegal profits made from such offences," said the paper.
The courts in Scotland and Northern Ireland operate differently from those in England and Wales, and there is no equivalent sentencing guideline system there, but the consultation suggests that those courts could still implement maximum fines.
"The court structures in Scotland and Northern Ireland differ from those in England and Wales, but exceptional statutory maxima could be introduced for summary courts in Scotland and Northern Ireland as for England and Wales," it said.
The consultation is open until 31 October.