Despite it being mocked by engineers, Leo Varadkar revealed he had discussed the concept with a “particularly keen” Mr Johnson and had told him it was worth examining.
Both Mr Johnson and the Democratic Unionist Party have previously spoken warmly of the idea, and just last week Mr Johnson ominously told MPs gathered in the House of Commons: “Watch this space.”
In the summer, government officials also probed where the money could come from and the risks around such a project, which are thought to include Second World War munitions littered in the Irish Sea.
But Mr Varadkar said he had also insisted the UK would have to pay for the mammoth project if it were to go ahead. “At which point he [Mr Johnson] suggested, ‘No, no, the EU is going to pay for it,” he said.
He added: “So that’s definitely not going to happen, because neither Northern Ireland or Scotland are going to be in the EU. But it was kind of half serious, half joking in a way.
“But all messing aside, I do think at the very least a high-level engineering assessment should be done as to whether it is a viable proposal.”
Other parties, however, have been less enthusiastic about the idea, with Ulster Unionist Party leader Steve Aiken saying investment was urgently needed in Northern Ireland’s infrastructure first.
Mr Varadkar continued: “I know people dismiss these things out of hand, but they used to dismiss the Channel Tunnel as well – the idea of building a tunnel between France and Britain – and I know what I see when I see a bridge tunnel between Denmark and Sweden, when you fly over New Orleans and you see 110 miles of bridge, it’s extraordinary.
“I think we need to at least check out is this viable in engineering terms and how much money it would cost to do.”
But Mr Varadkar said he is more interested in talking to Mr Johnson about other projects the two nations could work on together, such as a high-speed rail link connecting Dublin, Belfast and Cork, and better connections to the northwest.
“There are actually loads of really good projects we could do together that might not cost as much and would definitely be more feasible than a bridge between Scotland and Northern Ireland,” he said.
“But in my pursuit of those ones I’m not going to dismiss the one that the prime minister’s particularly keen on.”
One retired offshore engineer, James Duncan, previously described the building of a bridge in an article for The Times as “about as feasible as building a bridge to the moon”.
He wrote: “The trickiest section, Beaufort Dyke, was used for many years from 1946 to dump obsolete munitions. The Ministry of Defence estimates the total dumped at more than 1.5m tons. There are no maps of their locations.
“No sane contractor or responsible government would consider building such a bridge, and because of the weather conditions it would probably have to be closed for considerable periods if it did. The proposal is just another thoughtless soundbite.”