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 26-year-old was signed by Ian Holloway, who also worked with Grandin at Blackpool during the player's three-year spell.
Grandin only played one match during his time at Palace, the 2-1 defeat to Bristol City in the Capital One Cup last August.
"Crystal Palace Football Club can today confirm that Elliot Grandin has left the club by mutual consent," a statement from Palace read.
"Crystal Palace would like to thank Elliot for his services to the club and we wish him all the best for his future career."