The report stated that Galatasaray will meet with the Germany international’s agent to discuss his future.
The Istanbul giants signed Grosskreutz from Dortmund last summer but were unable to register the 26-year-old after failing to send over the necessary paperwork to FIFA before the transfer deadline.
Grosskreutz will not be able to play for the Lions until January when the transfer window opens.
Klopp is keen on getting to know his current crop of players but stated that under the right circumstances a winter transfer could end up being a possibility.
“It’s much more important to work with people and if you trust them they have to feel it – and not just for two days but for a longer time,” Klopp was quoted as saying in the Telegraph.
“That’s not how the world should run. If we have problems it’s not with quality, it’s maybe with concentration or other things. But we don’t know if players we get will do it better. I’d give the advice to stay cool and see what happens.
“If we need something we will do it, not talk about it before. In this moment I don’t think about it. No one should be in doubt that we are prepared for any situation. We have 24 hours always at work.”
Scottish giants Celtic have also joined the race for the World Cup winner according to the Scottsman.
The report claims that the the Lions are happy to let the former Borussia Dortmund man leave for a fee in the region of £1.8 million.