The Germany international is running down his contract at Anfield, with there no indication that he will be committing to fresh terms.
That situation has seen various landing spots mooted for Can, with Serie A champions Juve considered to be the most likely.
They have been leading the chase for a versatile performer heading towards free agency, despite failing to put an agreement in place.
It was suggested in American publication Sports Illustrated on Wednesday that a deal had finally been done, with Can destined to be heading for Turin this summer.
Their report claimed that sources had spoken with Khedira and received confirmation that the World Cup winner is to be joined at the Bianconeri by a fellow countryman.
That is, however, news to the man at the centre of the article, with the claims played down on social media.
Khedira posted on his official Twitter account: “A Sports Illustrated source heard me confirm Emre Can is coming to Juventus this summer. Only one possible explanation: I am having a secret twin brother don't know what Emre will do next season ...”
A Sports Illustrated source heard me confirm Emre Can is coming to @juventusfc this summer. Only one possible explanation: I am having a secret twin brother I don't know what Emre will do next season ... #shoutouttomymum #fakenews https://t.co/AnMyf4Ho9I pic.twitter.com/oBJ8vOg1kx— Sami Khedira (@SamiKhedira) April 5, 2018
Khedira, who joined Juve from Real Madrid in the summer of 2015, also branded the Can claims “fake news”.
There is, however, still a chance that a move will be made, as Can is now a matter of months away from the reaching the end of his current deal at Liverpool.
He has hit back at reports suggesting that excessive demands are to blame for the Reds’ inability to put an extension in place, but he has also offered little insight as to his future plans.