It is understood the Reds have already offered the Serbian outfit £5.8million for the promising 19-year-old who is also a firm target for German club Stuttgart.
"I will do my best to show respect to the club [Red Star], the public and the supporters, but then I think I need to choose the best environment for myself in which I'll get my chance and work with good coaches in good conditions," Grujic told Serbian outlet Blic.
"Maybe something will happen, but there's no rush. I am certainly staying there [Red Star] until the end of the qualifiers for the Champions League. That works for Liverpool too. We had talks and I haven't made any deal yet. I am still a Red Star player."