Klopp is in the market for a new keeper signing with Simon Mignolet ready to quit Anfield this summer.
BILD says Switzerland international Sommer is on his radar and he is having Reds scouts watch him during the World Cup.
Tied to Gladbach until 2021, Sommer can leave for €30m.
The club's football director Max Eberl stated last week: "At Gladbach, no player is unsaleable. Who knows what sums of money the Englishmen will beckon when one of our players truimphs in Russia?"