McGiveron is now playing for the reserves after graduating from the U18 team last season.
He told liverpoolfc.tv: "Throughout my life I've watched Jamie Carragher and I've always looked up to him from day one of my playing career. He's been a fantastic servant to this club and the perfect example of what a defender must do to be a success at LFC. He's the benchmark.
"I've grown up supporting Liverpool and always wanted to play for them. It's the old cliché, but it really is a dream to be here."