Mr Johnson was asked twice about the idea by Conservative Party members in Northern Ireland while appearing at a hustings event on Tuesday.
"I am an enthusiast for that idea, I'm going to put it out there, I think it's a good idea but again that is the kind of project that should be pursued by a dynamic Northern Ireland government championed by local people with local consent and interest, backed by local business and mobilised by the politicians in Northern Ireland," he said.
"That's what should happen. I'm all in favour of it but it's got to be supported by people here in Northern Ireland.
When asked by event chair Iain Dale about the financing of such a project, Mr Johnson responded: "With infrastructure projects, finance is not the issue, the issue is political will, the issue is getting the business community to see that this could be something that works for them, the issue is getting popular demand and popular consent for a great infrastructure project, and that is why you need Stormont."
DUP leader Arlene Foster and MP Sammy Wilson have both expressed their support for the building of a bridge to Scotland.
Meanwhile, Scottish First Minister Nicola Sturgeon did not rule it out earlier this year.
But speaking during a visit to Dublin in May, Ms Sturgeon said she believed there are other ways of strengthening relations between Scotland, Northern Ireland and the Republic of Ireland.
"We will always talk about how we can strengthen relations, we need to have practical and achievable ideas," she said.
"I have representations made to me about the idea of a bridge, there are obviously a lot of challenges and things to be discussed there.
"Whether it's around a bridge or in other ways strengthening the relationship between Scotland, the north of Ireland and the Republic of Ireland is a big priority for my government."
Last year, architect Professor Alan Dunlop proposed two options for the bridge which could connect either Larne and Portpatrick or Mull of Kintyre with Torr Head, and estimated the cost to be between £15 billion and £20 billion.