The Mirror says the 25-year-old is set for a £500,000 move to the Magpies in the January transfer window.
The former Leeds United star has rejected a offer of a new contract at Sheffield United.
Kilgallon will sign a pre-contract agreement with Newcastle and join them for free at the end of the season if Sheffield United does not let him join the Magpies in January.
Wolves, Wigan, Bolton, Celtic and Newcastle were reportedly ready to pay £4million for Kilgallon in the summer, but United snubbed all offers as they were confident he would sign a contract extension.
