The German veteran is off contract in June and talked up the prospect of a late career move to England last week.
Ancelotti worked with Khedira at Real Madrid, where they won the Champions League together at the end of the 2013/14 season. Now 33, Khedira is eager to play on after his contract with Juve expires in June - and admits testing himself in the Premier League is an ambition he's eager to fulfil.
For his part, Ancelotti cannot hide his admiration for the German and admits he is open to the prospect of working again with his former Real midfielder.
Ancelotti was quoted by TMW, saying to Sky Deutschland: “I have great memories of working with Khedira.
"In Real Madrid he showed himself as a real professional. I would love to work with him again, but he is not alone.
"There have been many great players in my career. However, moving here to Everton is another thing to think about."
Khedira has now been with Juve for five years, winning five Scudetti, three Coppa Italias and a Supercoppa Italiana. This season, he is yet to make an appearance for Andrea Pirlo's team.
- updated November 23