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 centre-back is nearing his 200th appearance for County and replaced Paul Lawson as the most loyal servant among the playing staff when the midfielder left for Motherwell earlier this week.
Boyd formed a solid centre-back partnership with Grant Munro for the majority of the season to help County finish fifth in their debut Clydesdale Bank Premier League campaign.
Manager Derek Adams told the club's official website: "I am delighted Scott has decided to stay with us next season as he has been a valuable player over the past six years.
"He joined Ross County when we were in the Second Division and now has a collection of medals to his name."