Mrs Foster said: "I think it is an event for the whole of Northern Ireland, looking forward to the future, looking forward to our young people having a place in the world and that is what I want to see happening for our centenary plans".
According to the RTE report, Mr. Johnson's visit was also meant to outline the first stage of Britain's 2021 plans to mark "the centenary of Northern Ireland's foundation" in May, 1921 following the partition of Ireland.
The bridge, between Portpatrick and Larne, would span 28 miles and cost in the region of £20bn to build, with Mr Johnson previously estimating the cost at around £15bn.
Ahead of his trip, Johnson said Britain would "stand side-by-side" with Northern Ireland.
Johnson will also discuss celebrations for the centenary of Northern Ireland's creation next year and will meet with the Republic of Ireland's new Taoiseach, Micheál Martin, to discuss the progress of Brexit talks.
"We look forward to a very warm engagement", he said.
He is due to meet the First and Deputy First Ministers this morning to discuss how they can rebuild the economy.
Mr. Martin, according to the RTE report, said there was a good focus on the British-Irish relationship in the context of Brexit and the two agreed to create new structures around the relationship to be ready post-Brexit.
"There will be no border down the Irish Sea - over my dead body", he added.
Northern Ireland's views on leaving the United Kingdom are still largely split along sectarian lines, with many Catholics favouring the creation of a united Ireland while pro-British Protestants favour the status quo.
Prime Minister r Johnson is also expected to meet First Ministers Arlene Foster and Michelle O'Neill to discuss an economic recovery plan, following the news that the United Kingdom has slipped into its worst recession on record.
"The last thing we all need now is a second significant systemic shock to our systems to our economic systems and that's what a no-deal Brexit would present on top of or alongside Covid", Mr Martin said.
"We remember John at moments like this because he did so much to facilitate these kind of meetings and make them much more regular in the normal course of events", Martin said.
Northern Ireland Secretary Brandon Lewis said: "The centenary is an opportunity to celebrate the people, places and products of Northern Ireland, which has such rich sporting, cultural, entrepreneurial and academic talent".
Shortly after arriving at the castle, the taoiseach joined the prime minister for a walk in the restored grounds of the royal residence and tourist attraction in an affluent village near Belfast.
