The Hammers have just banked a guaranteed £100m from selling Rice to Arsenal and are now expected to reinvest it in fresh faces.
Goretzka, 28, has been strongly linked with an exit from Bayern Munich, with the club open to offers to offload him.
And the Bayern Munich midfielder is on West Ham’s wanted list, according to Sky Deutschland, as a replacement for Rice.
Bayern Munich are looking for in the region of €40m to €50m to cash in on Goretzka.
While West Ham could likely afford to pay such a fee for the midfielder, they would have to work hard to sell a move to the player.
Goretzka has so far rebuffed approaches from other clubs as he wants to stay at Bayern Munich.
With Thomas Tuchel pushing to bring in a new midfielder though, Goretzka could soon be forced to rethink his position.
The experienced midfielder, who has won over half a century of caps for Germany, has also been linked with Manchester United.
