The Croatian midfielder is still on Liverpool's radar according to weekend reports.
The Reds are said to have been interested in the 20-year-old when he was on the books at RNK Split but he ultimately moved to Dinamo Zagreb this summer for £4million.
However, Liverpool are said to remain interested and are planning a second bid when they next have the chance, with the player now reportedly valued at around £8million.
Rog played 44 matches for Split, scoring nine goals and providing seven assists in that time. He has since scored two goals in 18 appearances for Zagreb and has helped them remain undefeated in the league so far this season.
Both his recent goals came in the Champions League qualifying rounds and given his age he is only likely to improve as the years go on.
That said, Liverpool already have plenty of young attacking talent and some Reds fans may feel it would be better to develop the players coming through their academy rather than bringing in yet another unproven footballer from abroad.