Italian outlet Calciomercato [via Daily Mail] suggest that the Premier League side are interested in signing Khedira, with the German said to be favouring a move to the English top-flight when the transfer window opens.
Everton coach Carlo Ancelotti has worked with Khedira before, between 2013 and 2015 while he was the Real Madrid manager, and will be aware of what the German midfielder can bring to the table for the Toffees.
Meanwhile, Khedira has not featured for Juventus in any games so far this season, and it looks unlikely he will feature for the Old Lady between now and the January transfer window opening.
Khedira, who won the World Cup with Germany in 2014, is said to be not part of Pirlo's plans, and Juve had reportedly tried to offload him last summer. CalcioMercato also add Pirlo has told the German he is free to leave the club.
The Italian outlet also note that although he has not played for Juve this season, he has been training regularly with the squad and is in good shape.
It remains to be seen who will sign the former Real Madrid midfielder should he leave in January, but wherever he goes, the 33-year-old would add immense experience to any squad.