The 27-year-old has been linked with a Premier League switch for much of the past few months after making a successful comeback from a lengthy injury lay-off.
Arsenal and Chelsea were thought to be the two sides to be set for a tug-of-war, but now Liverpool and United are also in the running.
Both sides are keen to bolster their midfield ranks, and see the experienced Khedira as a good option.
United recently snapped up Ander Herrera, but with the Spaniard considered to be a classy playmaker, a holding enforcer is now Louis van Gaal’s priority.
The Red Devils are understood to have tracked the player last year, and he could be a more cost-effective option that Arturo Vidal.
Liverpool are also interested despite their move for German youngster Emre Can.
Reports claim that if Luis Suarez is sold some of the cash brought in could help the Reds to fund a swoop.