The German veteran could be available on a free transfer this window.
The 33-year-old is close to terminating his contract with the Italian club, per Goal.com.
He is not in the plans of Andrea Pirlo, and Juve want his wages off their salary bill.
Khedira has suffered a lot of injury problems, which would make United's interest odd.
But the Red Devils do want another midfield option, and may see Khedira as an experienced candidate to play defensive midfield.