Gotze, once viewed as the poster boy of German football after scoring the winning goal in the 2014 World Cup final, has largely struggled since rejoining Dortmund from Bayern Munich in 2016.
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.
Grosskreutz says Gotze should seek a move away from the Westfalenstadion in January and could rebuild his career under the guidance of former manager Jurgen Klopp at Liverpool.
"I'm very sorry for Mario Gotze at the moment, because stuff is written about him - and only him - every day," Grosskreutz told Sky in Germany.