The Reds are contemplating a serious revamping of their central midfield options in the off-season.
Manager Jurgen Klopp is determined to challenge for trophies next season after a poor campaign by his standards.
Per BILD in Germany, the Reds are looking at Kone as a possible recruit for a modest fee.
The Reds' interest is described as being genuine and very significant, while they are prepared to pay between €40-45 million for his signature.
The Frenchman is a highly rated, box to box talent who is being linked to a host of top European clubs.