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.
Hyam, 20, would have been a free agent at the end of this season but manager Paul Jewell has opted to tie down the promising youngster on a further 12-month deal, with the added option of another year.
The academy graduate told Town's official website: "I'm obviously pleased to have signed a new contract. I've had one-year deals for a while so this gives me some stability.
"Everyone knows that Ipswich is my club and I grew up watching the team play and I'd like to stay here and play for as long as I can."
Hyam, who has recently been struggling with a back injury, has made five starts for Town so far this season. And he admits his new contract is even more special having questioned his own future at the club last term.
"I did think halfway through last season that I might have to move on," Hyam added. "I wasn't really playing any games and was a long way from getting in the first-team. I could have gone out on loan but decided to stay at the club and have managed to turn things around."