While Whitehall said no decision has been taken and the Government is still looking at the issue, it is understood it will not happen in the near future, if at all.
Alex Neil, Scottish Government Infrastructure Secretary, has written to the Treasury asking for an urgent update on the tax situation, which he and airport and airline bosses have branded a barrier to inward investment in Scotland.
He explained that the UK Government said in December it would investigate the feasibility of devolving power over the tax to Holyrood, but said nothing has happened since.
The Treasury says the door is not closed but there is no current formal consultation process over Air Passenger Duty (APD) and it will continue to listen to views on the subject.
The tax, which adds to the cost of air fares, has been devolved to Northern Ireland to allow air fares on long haul rates to be reduced.
A Treasury spokesman said: "Devolving APD could potentially distort the whole UK market, if for example rates were changed substantially in Scotland or Wales.
"In view of the risks, the Government will explore the issues more fully before making a final decision.
"The decision to devolve aspects of APD to the Northern Ireland Assembly reflects the unique challenges faced there, with competition across the border from a separate EU member state."
Scottish airports have said the high rate of the tax is preventing them attracting new routes and agree with the Scottish Government it should be devolved.
A spokesman for Glasgow Airport, said: "The UK currently has the highest rate of aviation tax in Europe and APD is proving a significant barrier to attracting new routes."
Mr Neil said he has written this week to the Treasury and said planned rises in APD will only make matters worse. He said: "Our airports and airlines are telling us on a regular basis that APD is eroding their ability to introduce new direct international air services.
"The case for Scotland to control APD is compelling, and is backed by all four of Scotland's major airports.
"The UK Government said in December that it would 'continue to explore the feasibility and likely effect of devolution of APD to Scotland' and I have written to them this week seeking an urgent update on that work."