The DUP want to build a bridge connecting Ireland with Scotland.
They say a 25-mile bridge, or tunnel, could be used to link the North with mainland UK.
The cost is estimated at £20bn (€22.7bn) and according to The Express newspaper would rank among the biggest infrastructure projects in British history.
A DUP spokeswoman said: "The bridge will act as a catalyst for developing further links between the two islands."
Senior DUP MP Sammy Wilson and former Stormont minister Simon Hamilton brought up the proposal.