The 22-year-old had attracted offers from the likes of Cardiff City, Crystal Palace, Middlesbrough, Lyon and CSKA Moscow, while Torino had a €10 million bid for a permanent transfer knocked back.
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Instead, the Serbia international has agreed to extend his contract at Anfield until 2023, but coach Jurgen Klopp wants him to spend a season away to gain more experience.
Grujic has 14 first-team appearances to his name with the Reds, who view him as a potential regular starter next season and will be expecting a strong campaign when he joins the side that finished 10th in the Bundesliga last term.
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Grujic joined the Reds two years ago from Red Star but was loaned back to the Belgrade side before spending the second half of last season at Cardiff, where he made 14 appearances.
He had hopes of getting into the Liverpool starting XI this time around, but the arrival of Naby Keita from RB Leipzig and Xherdan Shaqiri joining from Stoke City, competition for a place in midfield is tough.
“Everyone knows we bought two new midfielders, two great players and great guys,” he said last month.
“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.”
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