Gallant will spend four days in Alberta, where he will also meet senior TransCanada (TSX:TRP) officials in Calgary.
He says he also wants to meet with Alberta business leaders to show his commitment to the $12-billion development and help secure opportunities for New Brunswick.
Former premiers David Alward and Alison Redford made similar trips to each other's provinces when they were in office in support of the project.
If it proceeds, the Energy East Pipeline would ship oil from Alberta to refineries in Quebec, with a pipeline extension to be built to a refinery and export terminal in Saint John, N.B.
TransCanada is expected to file a formal proposal with the national energy regulator within weeks.