Prescott said TransCanada expects to finish the pipeline by summer, with an eye toward getting it in service in the fourth quarter.
The completed line will transport up to 700,000 barrels of crude oil a day from the storage hub at Cushing to refineries along the Gulf Coast.
The project is part of TransCanada's planned Keystone XL pipeline, which would move crude oil from Canada and North Dakota.
The overall plan was rejected by the Obama administration last year because of concerns about its route through Nebraska's vast Ogallala Aquifer.
The Canadian company opted to move forward with the Gulf Coast portion of the line to help reduce the glut of oil in storage at Cushing.
TransCanada since has submitted a new application for a permit for the proposed transcontinental pipeline.