The 27-year-old, who has spent his entire career with the Bundesliga club and has a further two years on his contract, revealed in June that he has recently turned down the advances of Arsenal and AC Milan.
Yet the World Cup winner has now revealed he would be interested in a move to the Premier League and spoke of his admiration of both newly named Liverpool manager Klopp and the Anfield club.
“A move abroad excites me. England would for sure be an interesting destination," he told Bild.
“Currently I am with Schalke. There are no deals sorted. But of course, for a footballer there are some clubs that are more interesting than others.
“English football is very fortunate to have someone like Klopp in the league, Liverpool is a club with great tradition and values.”