Gotze has suffered a significant decline since scoring the winning goal for Germany at the 2014 World Cup, failing to make the squad for this summer's tournament and falling out of favour with Dortmund too.
The 26-year-old has been limited to just two first-team appearances so far this season and was left out of the squad entirely for Saturday's match against Hoffenheim, having failed to impress in a Europa League clash with Club Brugge.
Grosskreutz believes that a reunion with former Dortmund boss Jurgen Klopp would be exactly what Gotze needs to kickstart his career once again.
"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.
"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."
Liverpool have regularly been linked with a move for Gotze in the past.