The midfielder is in the final year of his contract at Juventus, but he is not in Andrea Pirlo’s plans and the Italian champions have been working to offload him.
The Italian champions have been in talks with his representatives over the termination of his contract for several months, but no agreement has been reached yet.
But talks have continued to take place and, according to Turin-based Italian daily Tuttosport, the club are hopeful that an agreement can be worked out before the end of the year.
Juventus are keen to save around €5m to €6m from terminating Khedira’s contract and it would allow the player to find a new club in January.
He has been heavily linked with a move to the Premier League, with Everton believed to be the front runners to secure his signature.
The midfielder could be tempted by the prospect of a free transfer switch to Goodison Park in the new year.
Khedira worked with Carlo Ancelotti at Real Madrid and may be open to reuniting with his former coach at Goodison Park.
There is likely to be competition for Khedira’s signature if he is a free agent.