Joyce made three appearances for the Shrimpers in the recent campaign during the absence of regular goalkeeper Steve Mildenhall but it was enough to catch the attention of Tilson.
"We've offered Ian another year's contract. He did well when called upon in the first team last season but he knows he still has things to work on," Tilson told the club's official website.
"He's improving during the year with us and that is why we have decided to offer him a new contract.
"The ball is now in his court as to whether or not he decides to accept it."
Tilson has also offered a new deal to Peter Clarke and is currently in talks with the player's agent, adding: "We've started talking to him but I don't think we are going to get a decision straight away."