Tuttosport says the experienced midfielder could be available on a free transfer amid his exile from Andrea Pirlo's squad.
Juventus did not name Khedira, 33, in their Champions League squad and he is yet to play this season.
Talks are reportedly underway over terminating his contract, with no agreement reached yet. Manchester United and Tottenham have been linked with a move for Khedira.
But West Ham are also tracking the German.
Khedira has played only once in 2020 while suffering from knee and hamstring issues.