Publisher Guardian Media Group (GMG) said last year it needed to make savings of 20 percent to stem underlying losses that widened to 62.6 million pounds ($78 million) for the year to April 3. It said it was aiming to break even in three years.
"The company is working on a whole range of efficiency projects and the print programme fits into that," one source close to the company said on Monday.
GMG prints both the Guardian and its Sunday stablemate The Observer on special presses bought more than 11 years ago when it switched from a broadsheet to the mid-sized Berliner format.
Editorially, the left-leaning Guardian has clashed with Murdoch's British newspapers, notably in bringing to light the phone-hacking scandal that resulted in the closure of his News of the World tabloid in 2011
On a business level, however, the two groups are collaborating, along with Trinity Mirror and Telegraph Media Group, on Project Rio, a plan to pool newspaper advertising sales.
Daily Mail publisher DMGT pulled out of the initiative this month, according to reports.
"The discussions explored a number of other areas of co-operation," one source said.
Another source said GMG was considering a plan to move production to News UK's presses later this year, and change the format to a tabloid in the process.
Rival publishers' presses are set up to print in broadsheet and tabloid formats. The Berliner format can still be produced using cutting equipment, although it would increase costs, the other source said.
Any saving in production costs from moving to a tabloid if the group decided to change printers would need to be weighed against the cost of redesigning the paper, the source said.
GMG is owned by The Scott Trust, created in 1936 to safeguard its flagship newspaper.
The newspaper's scoops include US whistleblower Edward Snowden's revelation about mass surveillances as well as the phone hacking scandal, and its online edition is one of the most popular in the world.
A deterioration in the advertising market has led to widening losses, however, and the group cut jobs last year under a turnaround plan led by editor in chief Katharine Viner and Chief Executive David Pemsel.
The Guardian abandoned the broadsheet size in 2005, but unlike its rivals The Independent and The Times which went tabloid, it choose the Berliner, a format long established in continental Europe but little known in Britain.
GMG spent 50 million pounds ($62 million) on presses from German engineer Man Roland, according to a Guardian article published in 2009, and another 30 million on new print sites in London's Stratford and in Trafford Park in Manchester.
Print sales of the newspaper rose following the change and an associated redesign, but the boost was short lived.
Its average sale in October was 157,778 copies, according to ABC, fewer than half the number of copies sold in 2005, resulting in under-utilised presses.
A spokesman for the Guardian declined to comment on speculation regarding future print allocation.
News UK's NewsPrinters operation has sites in Broxbourne, near London, Knowsley in north-west England and Motherwell, Scotland, where it prints The Sun, The Times and The Sunday Times, as well as The Daily Telegraph, The Sunday Telegraph and the Financial Times for other publishers.
A News UK spokeswoman said: "NewsPrinters is an active industry printer and is always looking at new opportunities.
"However, we don't comment on any business matters that may relate to third-party contracts."