A paper prepared for councillors said the council may need to scrap its pledge not to make staff compulsorily redundant.
The figure is 1,000 less than the 3,000 job losses predicted by the Unison union on Wednesday.
But it is 1,000 more than the council itself warned of in June.
The council expects to save £126m over four years - more than previously forecast. It said it would seek volunteers for redundancy first.
Officials hope to cut the number of staff over the next two years but said they would save more if the cuts were achieved more quickly.
The City of Edinburgh Council has been run by a Labour-SNP coalition since 2012.
The forecasts are contained in papers to be discussed by the council's finance committee next Thursday.
The council said the workforce made up 60% of its budget and it would be "unrealistic" to make the required savings without reducing the number of employees.
Alasdair Rankin, the council's finance convener, said: "We are very clear about the scale of the financial challenge that the council is facing.
"The council is experiencing greater demand for services than ever before, with a growing population in Edinburgh and increasing numbers of older people and younger people, while our overall budget remains the same.
"We need to take action in order to achieve the necessary savings to meet this demand, and we are making every effort to do this in a way that will safeguard frontline services for the people of Edinburgh.
"We want to invest in the services that are important to the public but must also look to rationalise our spending where appropriate."
Mr Rankin said councillors recognised some the proposals "may involve tough decisions, including a reduction in council jobs, particularly in middle management".
He added: "While this won't to be easy, savings will allow us to prioritise the things that matter most to people.
"Our aim, as ever, is to improve and enhance the city for residents, and this package of measures is the next step to achieving this."
Responding to the announcement, Unison said councillors appeared to be considering privatisation of facilities management.
John Stevenson, from the union's Edinburgh branch, said. "Our view is that if this privatisation is being held up as a way of avoiding compulsory redundancies, it is a flawed idea and all we will end up with is the triple-whammy of privatisation, compulsory redundancies and ruined services.
"The continued drive by senior officials to introduce privatisation despite the council 'presumption' against privatisation is deeply worrying. Edinburgh needs to reaffirm its commitment to a public service culture and abandon the privatisation 'solutions' that have been so disastrous elsewhere.
The council revealed plans for an internal restructuring earlier this year to help it achieve its savings.
It said its budget had fallen by 14% in real terms since 2010.
There are no direct proposals for further cuts or changes to local services at this stage although councillors have conceded it was inevitable the public may feel the impact of the job cuts.
However, they have stressed their priority is to try to safeguard frontline services.
A number of reports, to be discussed by the finance and resources committee on 24 September, will propose cost-saving actions across the council.

Thethe Dow Jones closed 0.4% higher at 18,332.43, the S&P 500 rose 0.4% at 2,139.53 while the tech-heavy Nasdaq jumped 0.5% to 5,193.49.
Analysts said the number of shares being traded was lower than normal.
Banks are reported to have put extra staff on duty in case of volatility.
"It doesn't take much in order to move the prices," said Peter Jankovskis, co-chief investment officer at OakBrook Investments.
Despite fears over the outcome of what is expected to be a tight race between Hillary Clinton and Donald Trump, analysts said investors would be relieved that the long period of uncertainty had come to an end.
"No matter who is elected, it will end a tremendous divide and return focus to earnings and all the fundamentals that have been pushed to the sidelines in recent weeks," said Rick Meckler, president of investment firm LibertyView Capital Management.
The three main US stock indexes saw their strongest rise in over eight months on Monday after the FBI announced it would not press criminal charges against Clinton for her use of a private email server.
The most dramatic stock movement in the US was car hire firm Hertz, which fell over 20% after the company slashed its full-year profit forecast.
Edinburgh city council is warning 2,000 jobs could go over the next two years as it seeks to balance its books.
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US shares have risen slightly, erasing earlier losses, but investors remain wary ahead of the US presidential election results.