The Prime Minister has ordered his team to find out how much the bridge would cost, how it could be funded and whether it would make sense to build, it has been claimed.
Mr Johnson floated the idea while working as foreign secretary last year.
He told the Sunday Times: “What we need to do is build a bridge between our islands.
“Why don’t we? Why don’t we?
“There is so much more we can do, and what grieves me about the current approach to Brexit is that we are just in danger of not believing in ourselves, not believing in Britain.”
Before he could build the 28-mile bridge, he would need to find out if unexploded World War Two bombs were potentially buried in its path, which is a concern that has been raised.
Members of the DUP in Northern Ireland backed the bridge idea last year and the Department for Transport is said to have gone as far as writing up a paper on the plans, Channel 4 says.
It was claimed the bridge could potentially cost £15 billion and would run from Larne, Northern Ireland, to south-west Scotland.
But it doesn’t seem like Scottish Conservative members are keen, with Ruth Davidson suggesting the idea was not realistic.
Meanwhile, Mr Johnson’s decision to suspend Parliament until October 15 has been ruled “improper” and “unlawful” by three senior Scottish judges, who concluded it had been done with “the purpose of stymying Parliament”.
The judges at the Court of Session in Edinburgh said the prorogation was therefore “null and of no effect”.
The UK Government said it was “disappointed” by the decision and would be appealing to the UK’s Supreme Court.
A separate court hearing at the High Court in London rejected a case brought by businesswoman Gina Miller, ruling the decision to prorogue Parliament was “purely political” and therefore not capable of challenge in the courts.
This judgement will also be challenged in the UK’s Supreme Court.