The German worldwide is in the final year of his contract and despite Jurgen Klopp claiming that talks over a new deal were positive, the Daily Mail reports that Juventus are readying an offer worth £31m for the midfielder.
Can's wage demands have reportedly hampered talks between the German and Liverpool, but the midfielder insisted in March that this was not the case.
"That's a manager you want to play under and I'm no different to that, I like being passionate and trying to get everyone going".
'That means they're not the worst talks but until anything is done or signed there's nothing to say'.
Klopp remains upbeat; "Emre is a very important player for us", he said.More news: Bush's Best Baked Beans issues recall over quality issues
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"Emre is certainly one of them".
But Klopp remains hopeful that the Germany worldwide remains at Anfield following positive discussions ahead of his return to pre-season training. "We want to keep him and we are having good talks".
Marković was given a run out against both Tranmere and Wigan in the Reds' domestic pre-season fixtures but it seems as if this was nothing more than a chance to be displayed in the metaphorical shop window.
While hopes of Liverpool managing to sign midfield dynamo Naby Keita is becoming bleaker and bleaker with passing time, their own midfield general Emre Can's contract situation will add further worry to the fans.
Liverpool finished in fourth place in Klopp's first full season in charge of the Merseyside outfit to secure a return to the Champions League.