Promising stopper Cort (pictured) has featured in every game for The Shrimpers this season and is being rewarded with enhanced terms.
"Leon has been outstanding for us again this season," Newman told the club's official website.
"We've recognised that fact and we want to get him tied up for further years at this football club."
However, the news was not so good for Barrington Belgrave, Graeme Jones and Phil Whelan, who have been told they will not be with the Third Division outfit next season.
Newman feels it is time for the triumvirate to seek pastures new but conceded it was a tough decision to release them.
He added: "It's a decision that wasn't very easy to make but it's one that you do have to make in football.
"These three have been here and done a job but I feel it's now time for them to move on.
"Baz has been here for a couple of years, Whelan's been here for three and sometimes you need a fresh challenge."
