Relegation-threatened Livorno have sacked Domenico Di Carlo after just 88 days in charge and re-appointed Davide Nicola.
Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
The 20-year-old has linked up with the Dutch side until next June after learning his trade at Liverpool's academy in the past few seasons.
Adorjan moved to Merseyside from MTK Hungaria in the summer of 2009 and the Reds have allowed him to pursue some first-team experience in the Eredivisie.
The Hungarian has captained his country at a number of levels and underlined his potential with some impressive displays for Liverpool's U18 side.