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 striker moved to Sardinia on a permanent deal last summer after spending the previous season on loan with the Rossoblu but will now return to Brazil for family reasons.
"After more than two years with the Rossoblu, I leave Sardinia to return to Brazil and play in Santos," he told www.cagliaricalcio.net.
"It's a difficult decision, because I consider the Cagliari an important team with special fans. To them I extend my greetings.
"In Sardinia, I found love, respect, friendship from everyone: from the President Cellino, who always treated me with utmost respect, to team-mates, not to mention the technical staff as well."