The Serbian international spent the second half of last season on loan in the Welsh capital, as he helped the side gain promotion back to the Premier League.
Grujic has failed to nail down a place at Liverpool in his 2 years at the club, making just 8 appearances in the league in that time. He will find it even harder to get first team opportunities this season as Jurgen Klopp has made it a priority to strengthen his central midfield area, recruiting Naby Keita and Fabinho so far in the transfer window.
As a result, it seems to make sense for the player and the two clubs that he would make a move away from Anfield, and Cardiff manager Neil Warnock has made it clear that he is happy to have the 22 year-old back at the club.
"We spoke to Liverpool, I think everything is in the pipeline but no news yet, we like him." he told 'Sky Sports'.
However, veteran manager Warnock thinks that the deal is being held up because the player's agent is not keen on his client making a move, even if Grujic himself is open to it.
The 'Bluebirds' have acted swiftly to strengthen their squad ahead of their first season back in the top flight for 5 years, having made four signings that have cost almost £30 million in fees.
The club will get their Premier League campaign under way away to Bournemouth on 11th August.