The BBC understands the report suggests the number of UK workers unemployed due to non-EU immigration is well below the figure previously cited by ministers.
No 10 denied claims the report had been suppressed, saying it was not ready.
But it insisted it would be published in "due course", possibly within days.
The BBC's political editor Nick Robinson said the row over the report reflected splits within the coalition over the benefits of immigration, with the Lib Dems refusing to back a Conservative commitment to reduce levels of net migration to below 100,000 by 2015.
Home Secretary Theresa May has previously used research from 2012 by the Migration Advisory Committee (MAC), a group of independent academics, as a basis for saying that for every additional 100 immigrants from outside the EU, 23 British workers "would not be employed" as a consequence.
But the new analysis by civil servants is much less pessimistic, estimating that the cost to existing British workers of new arrivals is much lower.
Although the estimated figure for the so-called "displacement" of British workers has not been disclosed, Nick Robinson said he understood it was "virtually negligible".
He said the two reports were not directly comparable since the 2012 research covered a specific period between 1995 and 2010 while the new findings analysed all the research available on the impact of immigration.
But he said the row over the report's publication reflected fault lines within the coalition on the issue, with Mrs May keen to flag up evidence backing up her argument that migration has an economic "downside" while Lib Dem Business Secretary Vince Cable sought to do the opposite.
The BBC's Newsnight programme, which first reported the story, said it had been told by officials that No 10 had prevented publication of the report to avoid igniting controversy.
By Nick RobinsonPolitical editor
According to emails seen by Newsnight, the old research cited by Mrs May was not considered sufficiently "robust" by either the Treasury or the Department for Business.
The new report, it argued, had been checked by external academics and agreed across all the departments with a hand in migration - including the Home Office.
However, Newsnight said Home Office officials had protested that the new research, in parts, reflected an "institutional bias" in favour of migration among officials at the Treasury, Foreign Office and business department.
For Labour, shadow immigration minister David Hanson said the report would help inform the highly charged debate about immigration.
"The government's record on immigration is one of failing to meet their own net migration target and ramping up the rhetoric. Now they want to keep their own research hidden rather than scrutinised," he said.
"We need an open, calm and fact-based debate on the impact of immigration and this should be facilitated by the government and not made harder."
And economist Jonathan Portes, who questioned the validity of the 2012 research at the time, said there was no excuse not to release a report that was "purely analytical and is clearly of wide public interest".
Lib Dem MP Martin Horwood said the report had got "stuck in someone's in-tray" and should be "extricated", adding that the debate on immigration needed more facts and less rhetoric.
Downing Street said the report had not yet been completed but would be published "in due course".
It said the initial figures, compiled by teams at the Home Office and Business Department, had now been peer reviewed by academics, but that work had still to be completed.
By Anthony ReubenHead of statistics, BBC News
It's worth looking back at the caveats in the Migration Advisory Committee's (MAC) January 2012 report.
It does indeed mention the 23 jobs lost for 100 non-EU migrants number, but it also says there was no effect at all between 1975 and 1994, and while there was an effect between 1995 and 2010, it says that was fewer than eight jobs lost for every 100 migrants.
It also says that there is no effect at all in a buoyant economy, but few of these caveats have been seen in government references to this report.
So the new report, when it comes out, may not disagree that dramatically with the original one from MAC.
However, it said much of its findings supported the government's case for tighter controls on immigration.
And Sir Andrew Green, chair of the campaign group Migration Watch, said the impact of immigration could not be measured in purely economic terms and the effects on housing, transport and public services must also be considered.
"The best thing the government can now do is publish the report so that the public can see its limited scope," he wrote on the Spectator website.
Statistics released last week suggest the government is unlikely to meet its pledge to reduce net immigration - with numbers rising by 58,000 to 212,000 in the year to September 2013.
UKIP leader Nigel Farage said the Home Office should produce specific figures on the impact of EU migrants on UK workers' job prospects, saying this was now the most critical issue.
Labour has called for the immediate publication of a government report about the impact of immigration on the UK economy following suggestions that it has been withheld by Downing Street.