Marko Grujić, the Serbian 19 year old midfielder, has agreed terms on a 5 year deal with Liverpool.
Liverpool and Red Star Belgrade are now expected to complete the deal which will cost £5M.
Inter Milan were also interested in the player, but Klopp is believed to have been personally involved in convincing the player to move to Anfield.
However, the midfielder will be immediately loaned back to Red Star for the remainder of the season.
Grujić only became a regular member of the Red Star side last season, and is described by many as a box to box midfielder.
At just 19 years of age it remains to be seen whether he is to be a first team signing or another ambitious moneyball signing by Liverpool.
Red Star Belgrade are streets ahead in their domestic league - with a 25 points league lead. They have won 20 of their 22 games so far, drawing the other 2.
Grujić was a member of the Serbia side which won the FIFA Under-20 World Cup in New Zealand in summer 2015.
Grujić has been said, by many journalists with understanding of the league, to be the driving force in the team. Some football journalists have gone as far as noting the similarities between his playing style and that of Liverpool's former captain Steven Gerrard.