The series is take a two-year hiatus in 2014 and 2015, but will resume in 2016 at Utah.
"It seems that wherever I go during the summer, our fans and the BYU fans are interested in when we're going to play BYU in the future and where it's going to unfold," Hill said. "I can assure you that Tom Holmoe and I have had many discussions and we're very close to signing a contract."
The 2017 game will be played once again in September, but the 2018 is expected to be played on the last game of the season, pending Pac-12 approval.
"This is an opportunity for us to help the league by making sure that nobody has to play 12 games in a row," Hill said. "That gives us an opportunity to play BYU at the end of the year. We'll get a final approval from the league in early August, and then we'll make a formal announcement, if not sooner."
Dr. Hill said he realizes the significance of the rivalry game, and is doing everything he can to ensure it continues into the future.
"We value the BYU-Utah rivalry," Hill said. "We know it's important to our student-athletes, to our universities, to our fans and to the media."