On the eve of the winter meetings, the Dodgers appeared on the verge of re-signing the pitcher they viewed as the best of this free-agent class. The team was believed to be making progress toward a multi-year reunion with Rich Hill, according to people familiar with the situation. The people requested anonymity because no agreement had been finalized. Hill blossomed into stardom as a 36-year-old in 2016 after stints in the minors and independent baseball. His return would add a fragile but potent option to the team’s starting rotation and supply Clayton Kershaw with a left-handed partner to headline the group. As the Dodgers aim to shed payroll for 2017, the team has yet to determine solutions for vacancies at third base, second base and closer. The club will attempt to plug these holes as the industry gathers Sunday at the Gaylord National Resort and Convention Center outside Washington, D.C., for the annual week-long off-season junket. Bringing back Hill would help the Dodgers, but it would not fill the void created if Justin Turner and Kenley Jansen depart in free agency. The Dodgers may also pursue Aroldis Chapman as a replacement for Jansen. Hill posted a 2.12 earned-run average in 20 starts last season with Oakland and the Dodgers. In six outings after the Dodgers acquired him in August, he finished with a 1.83 earned-run average, 10.2 strikeouts per nine innings and a 7.80 strikeout-to-walk ratio. He threw seven perfect innings Sept. 10 in Miami.