Grujic is reportedly allowed to leave Liverpool for the bargain figure.
Liverpool are reportedly willing to offload midfielder Marko Grujic in the January transfer window after failing to make the breakthrough at Anfield, and Celtic cannot pass such an opportunity up.
The Sun claim the 22-year-old playmaker can leave the club for a bargain £4.5million, which would see the Reds take a loss on the player they signed from Red Star Belgrade for £5.1million (BBC Sport).
Grujic is currently on loan at Hertha Berlin in the Bundesliga until the end of the season, but the belief is that if a bid is made that meets Liverpool's asking price, he could be sold next month.
It is believed that Hertha are the likeliest to sign the box-to-box midfielder, though he has been limited to just six appearances this season due to an ankle problem.
But Rodgers is known for his ability to sign young players from English clubs and quickly turn them into first-team stars. Indeed, the likes of Moussa Dembele, Olivier Ntcham, Filip Benkovic and Patrick Roberts are just examples.
Raiding his former side to land Grujic would be an excellent bit of business, with the Serbian midfielder certainly capable of producing the kind of quality that would see him shine in the Scottish Premiership - and in Europe.
Though he is worth only £4.5million, consistent first-team football and the chance to make a name for himself would surely see his value increase and turning out for Celtic would give Grujic that chance.
It means signing him for such a small fee would give Celtic a player with plenty of resale value - especially as he is only 22 years of age. He is a must-buy for Celtic, if Rodgers can engineer a move.