"Our assault groups are working to secure positions on the outskirts of Kupyansk," Ganchev said.
He added that offensive operations continue to the northeast and southeast of the city.
"A fairly large grouping of Ukrainian forces may find itself in a partial encirclement," the regional head noted.
Earlier in November, President Vladimir Putin announced that Russian forces had encircled two enemy groups in the Kupyansk direction.
One of the groups, made up of about 10,000 troops, had been pressed against a reservoir, while another group of around 5,000 Ukrainian soldiers was trapped in a separate area.