Liverpool, Bayern and Barcelona are all in the running to sign Goretzka, who could leave Schalke this month.
The Germany international is regarded as one of his country’s hottest prospects and a move away beckons, with just a few months remaining on his Schalke deal.
Earlier this month, reports claimed the player had agreed a deal with German giants Bayern Munich.
However, the Sunday Mirror have dismissed these claims and say Klopp’s influence could yet see Liverpool land the 22-year-old ahead of their European rivals.
It is said Goretzka is yet to decide his future.
Speaking last month, the midfielder admitted he needed time to consider his options.
“I have to find out for myself what the next step should be,” Goretzka said.
“I have to consider a million things. I am a person who is very meticulous in such decisions. I play through all the scenarios. So I need time.
“There doesn’t exist a deadline, but I think we are in the final phase.
“The final decision will be made in January.”
And the Sunday Mirror say a move to Liverpool may be on the cards.
The Reds have been told they remain in with a chance of signing him, due to his admiration for Klopp.
Whether or not they secure his signature, however, remains to be seen.