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 32-year-old winger, who has won 11 caps for Northern Ireland, scored eight goals in 24 games for the Scottish Premiership club after leaving Hibernian for a second time in January.
A club statement read: "Ross County Football Club have mutually agreed to terminate the contract of Ivan Sproule with immediate effect due to personal and family reasons and his desire to return to Northern Ireland.
"Ross County would like to warmly thank Ivan for his contribution to the club as a player and wish him and his family all the very best for the future."
Sproule's last match for County saw him sent off for a reckless tackle in a 2-1 defeat by St Mirren on November 17 and he was suspended for the William Hill Scottish Cup fourth-round clash with Hibs on Saturday.