A feasibility student examining whether the project was possible is expected to advise against going ahead with plans for the bridge, with the government expected to agree with the recommendation.
The cancellation of the project comes as the SNP called for Scotland to receive a share of the estimated £20bn the bridge would have cost to build.
The party’s Westminster leader, Ian Blackford, labelled the plans “daft” but claimed the money for the bridge “can and should be made available”.
The recommendation to cancel the project is expected to be confirmed with the publication of Sir Peter Hendy’s Union Connectivity Review.
Ministers asked the transport expert to examine the links between the four nations of the United Kingdom and to recommend projects to improve public transport connections.
It is likely to recommend significant infrastructure upgrades to potential projects such as the extension of the Borders railway to Carlisle.
The so-called ‘Boris bridge’ between Northern Ireland and Scotland was being considered as part of this review, but officials are said to have ruled it out due to high costs and the engineering challenges involved.
Parts of the Irish Sea are as deep as 300m in some parts, meaning it could be difficult to sink support towers into the seabed, while there is also concerns around the fact the area was used as an ammunition dump during the Second World War.
A government source told the Sunday Telegraph: “Hendy has examined if this is affordable and practical and he concludes it would be technically very challenging.
"That's not to say it won't become viable at some point, but at the moment it would be very, very difficult and expensive."
Two links were suggested for the bridge, either linking Portpatrick with Larne, or near Campbeltown to the Antrim coast.
The Department for Transport said Sir Peter’s report will be published “shortly”, but its contents have sparked a row over ‘power grabs’ in Holyrood.
Earlier this year, the then cabinet secretary for transport, Michael Matheson, said money for infrastructure improvements in Scotland should go through existing channels and not come from the connectivity review.
In October, Alister Jack accused the Scottish Government of “irresponsible nationalism” around the review, with claims it was “not working with us, I think, just for the sake of being different”.
The SNP's Ian Blackford said the money previously earmarked by the bridge proposal should now be split between Northern Ireland and Scotland.
He said: “Let’s be honest, Boris Johnson’s plans for a bridge between Scotland and Northern Ireland were daft – but the funding that was suggested for it can and should be made available.
“It could then be spent on transport and connectivity projects that are worthwhile and deliverable – and compatible with our climate obligations."
The cancellation of the bridge between the two countries also follows the decision by the UK Government to scrap the eastern leg of HS2 which was set to go to Leeds.
This would have reduced journey times between Edinburgh and London, but new plans to upgrade the East Coast Main Line instead are set to deliver some improvements to journey times, but still less than originally promised.
The government has said HS2 will reduce journey times between Glasgow and London by around 40 minutes.