The Prime Minister has previously talked up the creation of a fixed link to boost connectivity, but it is understood the idea has been scrapped as it would be too expensive and technically challenging.
A feasibility study led by Network Rail chairman Sir Peter Hendy found that a bridge would cost an estimated £335 billion, while a tunnel would be around £209bn.
Sir Peter said the price of either project “would be impossible to justify” as “the benefits could not possibly outweigh the costs”.
A bridge or tunnel would be the longest structure of their kind ever built and take nearly 30 years to complete.
Sir Peter concluded it was “technically feasible to construct, maintain and operate” a tunnel or bridge, but recommended that no further work should be carried out due to the cost.
Criticising the idea, Lib Dem MP Jamie Stone said: “Domestic aviation, rail, and roads are being allowed to collapse, but Johnson just wants to play SimCity with taxpayers’ money.
"We don’t need any more vanity projects from Boris. What we need in the North is our locals airports to stay open and our crumbling roads to be fixed.
"When it comes to Northern Ireland, the Prime Minister is shamelessly tone deaf. I imagine that security and clarity for businesses – instead of grandstanding and threatening to trigger Article 16 – would be higher up the list of priorities than this shiny new bridge.”
Labour's shadow transport secretary Jim McMahon called for Mr Johnson to come up with realistic suggestions.
He said: "Given this is the second pie-in-the-sky bridge project the Prime Minister has failed to get off the ground, it's probably time to accept the joke is wearing a bit thin.
"His actions, or lack of, on transport in recent weeks speak much louder than the empty words and broken promises we have come to expect from this government.
"If the Conservatives are in any way serious about meeting our climate targets they need to work with leaders across every region and nation to come up with realistic solutions to improve connectivity and future proof our transport networks, not waste time on unworkable ideas."
Mr Johnson has pledged to create a strategic transport network across the UK following a wider review of connectivity by Sir Peter.
One of the key recommendations of the report is to create a UKNet, which would map out strategic locations across the country and plot how to link them together, while providing extra funding for underperforming areas of the network.
In Scotland, Sir Peter recommended reducing journey times and increasing capacity on the West Coast Main Line as well as routes between Scotland and London, and conducting an assessment of the east coast road and rail corridor.
Upgrades to the A75 in the south of Scotland were also recommended, which would improve connectivity to Northern Ireland, while calls were made for improving the A55, M53 and M56 and the South Wales Corridor in Wales, along with the North Wales Coast Main Line and rail links to the Midlands from Cardiff.
A Scottish Government spokesman said: “Transport is devolved to Holyrood and the UK Government should respect that.
“We will always seek to engage constructively with the UK Government – for example, on cross-border rail and our shared desire for HS2 to serve Scotland – but UK ministers have no role in deciding investment in Scotland’s trunk roads.
“Scottish ministers have not been sighted on the recommendations of the Union Connectivity report. However, if UK ministers really want to play a helpful role, then they could simply deliver the funding we need for such infrastructure investment in line with established budgetary mechanisms for Scotland to determine our spending priorities.”