The Reds are looking to rebuild their midfield options following a season which saw them finish outside the top four and fail to seriously challenge in any of the cup competitions.
Alexis Mac Allister has been signed, but Liverpool are keen for more midfielders and do have an interest in Kone.
However, according to Sky Deutschland, a switch to Anfield for Kone at present is unlikely.
While he is on Liverpool’s shortlist, he is not someone they are urgently working to sign.
Borussia Monchengladbach could cash in on Kone this summer, but have received no offers so far.
The Bundesliga club value Kone at in excess of €30m.
All eyes will be on whether Liverpool do try to take Kone to Anfield or concentrate on other candidates to add to Jurgen Klopp’s midfield ahead of a season where they only have Europa League football on the agenda.
