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 19-year-old, who has captained the club's reserve teams, has made 11 senior appearances since turning professional in the summer of 2011.
Thompson was sent off at Reading last season on his first start under Neil Warnock, but the Whites manager is delighted to have extended his stay with the club and says he is considering a loan option to assist with his development as a player.
"We've got high hopes for Zac," Warnock told the club's official website. "He is a young lad who will have to go out on loan and get some games and see how the real world is.
"He's had a taste of the first team at the end of last season, now we need to get some games lower down and some experience. I always remember when I first signed Paddy Kenny I loaned him to Whitby Town and it makes you a bit more aware of the situation.
"We've got every faith in Zac that's why we offered him the contract. With Green coming back after the international break and Norris back now, this is a good time for Zac to get some games."