Gotze, who scored Germany's World Cup winning goal against Argentina in 2014, has since struggled to kick on.
The 26-year-old has made just two first-team appearances for the club this season and was left out of the squad to face Hoffenheim on Saturday after a lacklustre performance against Club Brugge in the Europa League.
Former BVB team-mate Grosskreutz has backed Gotze to be leave Dortmund and reunite with his former manager, Jurgen Klopp.
"I'm very sorry for Mario Gotze at the moment, because stuff is written about him - and only him - every day," Grosskreutz told 'Sky Deutschland'.
"In Brugge, for example, the whole team didn't play well.
"Maybe it would be good for him to go abroad in the winter to find a bit more peace and bring his career back on track. Klopp knows him quite well, he would be a good fit for Liverpool."
June 10, 2018