His particular style of defending has brought back memories of Woodgate's performances in a Leeds shirt.
The 19-year-old has quickly adapted to life in the Premiership following his promotion to the first team after a long-term injury to Lucas Radebe.
The South African could be out for two months and caretaker boss Eddie Gray was quick to give Kilgallon the vote of confidence by plunging him into the fray against Aston Villa on Boxing Day, where he faced the toughest challenge of his short career when he came up against the in-form Juan Pablo Angel.
Kilgallon is now preparing for an even harder task, marking Arsenal's Thierry Henry in Sunday's FA Cup Third Round tie at Elland Road.
"I'm looking forward now and taking things from there," said Kilgallon. "I just have to keep playing as well as I can and hopefully I'll have a run of games and stay in there.
"It's nice to be compared with Woodgate, but I am my own player," he added.
"Being compared with him is something I like because he was a great player here.
"West Ham was good experience but, having come back here, I want to be involved."