The 34-year-old defender was an option for a short-term deal at St James' Park as Alan Pardew looks for cover in the heart of his defence.
The ex-Toon defender moved to Goodison Park in a £5million deal from Portsmouth in 2009 and has made 91 appearances to date.
The Frenchman's contract expires at the end of the season and under the terms of his deal he could sign a pre-contract agreement with a foreign club during the January transfer window.
Reports had earlier suggested that Distin had been holding out for a two-year extension on his current deal, rumours that were subsequently denied by the player.
David Moyes: "We have an option on Sylvain, so he can't go anywhere.
"It's not a problem."