Grujic made 14 appearances in 18 months for the Reds before joining Neil Warnock’s side on a half-season deal last week.
He is set to take up a focal role at Cardiff, with Warnock revealing “I’m not signing him to make the numbers up,” and the Serbian made his debut in Saturday’s 0-0 draw with Sheffield Wednesday.
But after a potentially fruitful spell in Wales, Grujic will return to Klopp’s squad, with the 50-year-old planning for his future role at Anfield.
“We miss him already in the training group because he developed really in a fantastic way,” he told LiverpoolFC.com.
“But because of the quality we have in the squad, it happened really often that he was not even in the squad.
“That’s not nice and he needs these 20 games in the Championship. I’m really happy for him.
“We had a long conversation about it and he’s looking forward to it. He wants to be a Liverpool player and I want him to be a Liverpool player.
“He gets the opportunity to play at Cardiff. It’s a difficult league as we all know.
“They are in a good position and maybe they will have play-off games, which would be a fantastic experience. So it’s a very good decision.”
Warnock spoke openly about Grujic’s opportunities at the Cardiff City Stadium, saying “we’ve got 19 games [left] and hopefully he’ll play in all of them,” which is an ideal situation.
He was part of the Bluebirds’ starting lineup for the weekend’s trip to Hillsborough, and played 78 minutes before being replaced by Callum Paterson.
Interestingly, Grujic was fielded in a midfield two alongside Joe Ralls, tasked with providing stability alongside the more progressive Englishman.
True to type, the 21-year-old picked up a yellow card within seven minutes, with Klopp no doubt hoping he will improve his discipline off the ball during his time at Cardiff.
And while overall he didn’t make a major impact, Grujic can be encouraged by his first outing for his new club, with the next five months pivotal to his development.
Returning to Merseyside for pre-season, he can then set his sights on carving out a more regular role under Klopp at Liverpool.