A loan spell back at Red Star was followed by another temporary switch for the first half of 2018, this time to Cardiff, where he scored once in 13 Championship outings.
Now back training with Liverpool during pre-season preparations in the United States, the Serbian signalled his intention to stay.
"I will speak about my situation with the manager and Michael (Edwards) over the next few weeks," Grujic told reporters when asked if he would return to Cardiff.
"I am now a Liverpool player and I want to show the best of me to Jurgen. After this tour we have a training camp in France. I will try to show my best and then we will see what happens."
But Grujic insisted that he is not daunted by the challenge of carving out a place in Klopp's plans.
"Everyone knows we bought two new midfielders, two great players and great guys," he added.
"There are a lot of players in my position so we will see what happens in the next few weeks.
"Of course I would rather go somewhere to play rather than just stay here and sit on the bench and only play for the under-23s. It's the decision of the club and what they decide is best for me I'll go along with."
One great way of convincing Liverpool of his talents, of course, would be a starring performance if given the chance against United, when the two rivals meet in Saturday's ICC game.
"It's always very interesting when we play against Man United. I'm really looking forward to it," Grujic said.
"It might only be a friendly game but we still want to beat them. We'll travel to Michigan and prepare to face United."