The latest number - if correct - significantly overshadows the 1,000 job cuts already flagged by the airline in December.
Here's my analysis from this morning's edition of AM.
The struggling carrier is under pressure to restructure its finances as it seeks a debt guarantee from the Federal Government.
However Qantas says it will not comment on the latest job cut figure reported by News Limited tabloid newspapers, which quote an unnamed Qantas source.
"There is lots of speculation about what things we will or won't announce on Thursday, but we're not in a position to comment on that speculation," a Qantas spokesman told the ABC.
"We have said that we will be making some tough decisions in order to achieve $2 billion in cost savings over the next three years, which is a consequence of an unprecedented set of market conditions now facing Qantas."
Recent speculation on the number of looming job cuts at Qantas has swung widely, ranging from 2,000 to 6,000 with one specific figure of 2,670.
Qantas maintains those numbers are "unsubstantiated and unsourced" but cuts are necessary to remain viable.
The airline's stance means two more days of unsettling uncertainty for the 33,000 people employed by Qantas and its subsidiary Jetstar.
Qantas issued a profit warning in December and said more than 1,000 additional jobs would be going over the next 12 months.
The airline has repeatedly said that "everything is on the table".
Renegotiating terminal leases in Melbourne, Perth and Brisbane to save hundred of millions of dollars could be one option considered.
Qantas has been quick to correct a number of rumours circulating about how it will cut costs, saying it will not be dropping routes from Dubai to London or Sydney to Johannesburg.
The Federal Government, particularly Treasurer Joe Hockey, will be closely watching as they consider the request for a debt guarantee.
Qantas does appear to be edging closer to getting that guarantee; effectively borrowing the Government's sovereign debt rating to raise money on global markets.
The airline lost its investment grade status late last year when the big two ratings agencies downgraded it to junk.
Qantas says it will press ahead with the cost reductions regardless of whether the Federal Government decides to help.
The Qantas share price has lifted since changed language from Mr Hockey and the Prime Minister signalled a Government guarantee was possible.
Qantas shares closed at $1.24 yesterday after falling to 96.5 cents in December after the profit warning and downgrade to “junk” investment status.