Other ideas include a “digital licence fee” – paid for by big tech companies and internet providers – and publishing data on BBC employees’ social class.
The Conservatives said the “internet tax” would increase consumers’ bills.
Low levels of trust in the media cannot be ignored, Mr Corbyn said on Thursday in the Alternative MacTaggart lecture – a speech which could be a guide to how a Labour government might approach media policy.
The Labour leader, who has been subject to fierce attacks by sections of the British press and has criticised leading tech firms over tax avoidance and data misuse, claimed journalists are being “held back” by media tycoons and, in the case of the BBC, by excessive state influence.
Without greater investment in investigative, public interest journalism, there is a risk that a “few tech giants and unaccountable billionaires will control huge swathes of our public space and debate”, he said.
Existing not-for-profit news organisations, like the Bureau for Investigative Journalism, should be given charitable status, he said, while new “news co-operatives” could be created with a remit to report on local government, private contractors operating public services, and regulated bodies.
These, he argued, could be paid for either through a content sharing and advertising revenue agreement with Google, similar to that agreed in France or Belgium in 2013.
If it is not possible to “tap up the digital monopolies that profit from every search, share and like we make”, he said a Labour government would be prepared to explore a one-off tax on the profits of the market-leading search engine and other platforms.
“The best journalism takes on the powerful, in the corporate world as well as government and helps create an informed public,” he said.
“This work costs money. We value it but somehow that does not translate into proper funding and legal support.”
Mr Corbyn has long supported a review of media ownership rules amid longstanding concerns within the party about the power of companies such as Rupert Murdoch’s News Corp and 21st Century Fox.
Labour’s 2017 manifesto promised to give regulator Ofcom more powers to protect media plurality and to reconsider rules on who is fit and proper to run TV and radio stations.
The speech did not refer specifically to ownership rules or to the current takeover battle for Sky or the future of Sky News – set to change ownership as part of the deal.
The hashtag #ChangeTheMedia has been used more than 9,000 times on Twitter since Mr Corbyn’s ideas emerged.
Ideas for the BBC
There are a series of proposals for the BBC, including publishing the social class of “all creators of BBC content, whether in-house or external”.
Responsibility for deciding the licence fee could be taken away from ministers and handed to an independent body.
He also made the case for a digital top-up to the licence fee, to be paid for by a levy on tech giants and internet service providers, to supplement the existing licence fee with a view to reducing the cost for poorer households.
BBC staff and licence-fee payers could get to elect some members of BBC national and regional editorial boards – which he said would reduce political influence and empower licence-fee payers.
The Conservatives said Labour’s proposals were economically illiterate and would hurt consumers.
“Tech companies would just put up their prices and pass this Internet Tax straight onto families and businesses across the country – adding more pressure to weekly bills,” said its deputy chair James Cleverly.