Brendan Rodgers is still in the market for creative talent, having already added Daniel Sturridge to his Anfield ranks during the January transfer window.
Ilicic was rumoured to be among those under consideration by the Liverpool coaching staff, with the Slovenia international having shone in Serie A since moving to Italy in 2010.
Speculation has suggested that an offer could be put to Palermo in an effort to test their resolve, but Ilicic's representative has sought to play down talk of a possible transfer being put in place.
"Ilicic moving to Anfield? Please, I don't know anything at all about that," Amir Ruznic told Ekipa.
"I haven't spoken to anybody about such a move.
"Palermo would not want a transfer to happen. I had a meeting with Palermo boss Maurizio Zamperini and he doesn't want to hear about this kind of scenario."