The Telegraph reported that executives at The Guardian and The Observer publisher Guardian News & Media want to end its print edition and focus on guardian.co.uk.
The report claimed that Rusbridger wasn't entirely on board with the idea and wanted to develop the paper's digital-only US venture before ending the print edition, to use it as a blueprint in the UK.
Trustees of the Scott Trust, the owner of GNM's parent company Guardian Media Group, allegedly feared that the company didn't have enough cash to sustain the newspapers for that long.
However, Rusbridger has since tweeted: "Telegraph story abt The Guardian simply untrue. Largely copied from [More About Advertising article]. Also untrue."
Guardian News & Media has been trying to cut losses of around £44 million a year, with any savings made being invested into expanding its US and online operations.
Its digital revenues increased to £45.7 million last year, but its overall operating losses rose to £31.1m.
Parent company Guardian Media Group, which also owns stakes in Trader Media Group and Top Right Group (formerly Emap), doubled Its operating losses to more than £129.1 million after almost £55 million of write-offs.
The Guardian newspaper has already axed some supplements in a cost-cutting exercise and has vowed to axe up to 100 of its 650 editorial staff. So far, not enough people have volunteered for the payoff package.
GNM had previously looked at closing its £80 million printing plant and moving the Berliner printing presses to Trinity Mirror's Watford plant.