Despite critics saying it would be a waste of time, Boris Johnson's official spokesman said the project was a "proper piece of work" that a "range of officials" were already looking into.
Downing Street said Boris Johnson - who is known to be a fan of bridges - was "ambitious" about infrastructure projects and is "looking at a wide range of schemes across the UK which could improve connectivity."
Mr Johnson has repeatedly spoken about the prospect of a bridge, even though experts have warned that the depth of the Irish Sea and the presence of dumped munitions would cause problems for any project.
The project could cost a reported £20 billion, although Mr Johnson has previously said it would "only cost about £15 billion".
The Prime Minister's official spokesman said: "The PM set out this was an idea which he believed could have some merit so, as a result of that, you would expect the Government to be looking into it."
The scoping work is being run from Number 10, with a range of officials reporting into it.
The Prime Minister told MPs "watch this space" when asked about the prospect of a "Boris bridge" in Parliament in December 2019.
The distance from Larne to Portpatrick, one of the most likely routes for a bridge, is around 45km.
There is no problem with distance, money or the Beaufort's Dyke explosives disposal area, according to the Prime Minister.
In November 2018, he said: "The problem is not the undersea Beaufort's Dyke or lack of funds. The problem is an absence of political will."
The new plan is the latest in a list of bridge projects suggested by the prime minister.
When London Mayor he infamously began a huge project which would have seen a "Garden Bridge" - decorated with dense flora - erected across the River Thames - the plan was eventually abandoned.
Then, when Theresa May's foreign secretary he suggested building a bridge across the English Channel which would connect Britain with France - the project never got off the ground.
On the latest bridge, government sources say it will be possible to build it with a tunnelled section to cope with some of the difficulties caused by the depth of the Irish Sea.