Liverpool were believed to have agreed a fee with Red Star Belgrade for the transfer of the 19-year-old last month but the confirmation of the switch has been delayed by work permit issues.
However, the player himself now looks to have revealed that his transfer is set to go ahead on Monday via a post on his official Facebook page.
Grujic posted: “On 4 January I will become a Liverpool player.”
It is believed that the teenager will go straight back on loan to Red Star Belgrade until the end of the season before joining up with his new team-mates next summer.
The Daily Express reports that the deal will be worth £5.1m.
The news comes after Liverpool kicked off 2016 with a disappointing 2-0 Premier League loss at West Ham United on Saturday.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news