The German is out of contract at the end of the season and is currently considering all of his options.
Because Can is in the final six months of his contract, he is allowed to sign a pre-agreement with a foreign club.
And Juventus were rumoured to be considering tabling an offer to the 24-year-old.
However, Liverpool are desperate to keep hold of the midfielder and they might have struck lucky as it appears the Serie A champions have turned their attention elsewhere.
According to the Daily Mail, Juventus are now chasing Arsenal’s Jack Wilshere.
The England international’s current deal expires in June and would be available on a free transfer.
Wilshere has not travelled with the Gunners squad to face Ostersund in the Europa League this evening (6pm).
The 26-year-old reportedly earns £100,000-a-week but Arsene Wenger is only willing to offer him a lower deal to stay on in north London.
The former Bolton loanee’s injury record could put Juventus off, but if they take a gamble Liverpool boss Jurgen Klopp will breath a huge sigh of relief.
The manager has previously expressed his desire to keep hold of Can.
“Emre is here in the moment and that is the most important thing,” Klopp said.
“We have to create a situation where players want to stay – that’s all we can do as a club, as a team and me as a manager.
“For me, there is no problem if Emre plays like he is in the moment.”