The Sun says the club have narrowed their list down to Koch as their key target for the January window.
Koch is 23 and is already one of the most impressive defenders in the Bundesliga.
While Caglar Soyuncu has admirably replaced Maguire in the starting lineup, Leicester know they must add competition for places to keep everyone on their toes.
And given his age, Koch would be one for the future.
He has helped Freiburg to reach the dizzy heights of fourth place in the league so far this season.