The Merseyside club completed the signing of the 19-year-old this month for a reported £5.1million.
Grujic has played a key role in helping Red Star amass an unassailable 25-point buffer at the top of the Serbian Super Liga and is now chasing the title while back on loan with the club her debuted for in 2013.
"I guess they understand me, they put themselves in my position, and after the title with my beloved club, I will be full of confidence to have success in Liverpool.
"Klopp also told me to stay focused in the next six months, to watch out what I eat and not to rest more than two to three weeks after the season.
"Then we have the pre-season tour in America."