Black Cats boss David Moyes was hoping to lure Jagielka to the Stadium of Light but Koeman has ruled out any potential of a departure for the England international.
"We had to get a new defender and Ashley brings experience, leadership and he knows the Premier League," Koeman said.
"Phil Jagielka is the captain of the team.
"We don't have too many centre-backs. We need four so there is no way he can leave the club."