Sokolov's career highlight was the 1987 World Championship cycle, where he reached the final of the Candidates Tournament. After qualifying through the Interzonal and round-robin Candidates Tournament, he won matches against Rafael Vaganian (6–2), and Artur Yusupov (7½–6½). However, in the final however he lost to Anatoly Karpov, 3½–7½. Having beaten Karpov at Bugojno 1986, he felt his pre-match mood had been overly optimistic and described his defeat as "very severe".