The Palermo attacking midfielder was apparently the subject of a Reds scouting visit when they watched the Sicilian club's Serie A games against Genoa a fortnight ago.
However, Ilicic has claimed that he is used to speculation regarding his future and insisted that his immediate focus is on life at Palermo.
"New rumours about my future? Nothing new, everything is quiet on this front. It is normal for me that there are rumours. One day you are linked with one club, another day with another club," the Slovenian told Sport Press.
"That is normal, but I am still at Palermo. I am only thinking about my team. The summer is well over and the transfer window reopens in January, which is far away.
"Now I am a Palermo player, I don't know what will happen in the future. We will see."
The 24-year-old moved to Italy from native side Maribor for a £2m fee in 2010.