The quartet will be out of contract in the summer with winger Wagstaff ending a 15-year association with the Addicks after making his final appearance in Saturday's 4-1 win over Bristol City at The Valley.
Former Stoke striker Fuller did not feature against the Robins while midfielder Kerkar and centre-half Taylor were unused substitutes.
Boss Chris Powell told the club website: "Scott has been superb since I walked through the door as manager, but I'd already got to know him as a young player during my playing days.
"He is now at the stage where he needs to get his career going. He was an integral part of our League One campaign, playing in a number of games and scoring a number of goals, but this year has been harder for him with regards to playing time.
"(Fuller) was disrupted by a number of injuries which, at times, halted his rhythm, but he's a real character who boasts plenty of experience.
"He remains very popular among the players here, but from the club's point of view, every aspect has to be assessed with regards to new deals.
"Matt is a player I could quite easily keep in and around the squad," said Powell. "I know for a fact that he wouldn't let anyone down or let this football club down. He is now at a stage when he needs to get as much playing action as he can from his career, and I just can't promise him that.
"It's quite easy to forget Salim's contribution this season. Since the turn of the year he has not featured much, but he was integral in the early part of the season and he had plenty of assists, and even had to play left-back when we had a number of injuries. He did very well for us so we wish him well in the future, as we do all those who are leaving us."
- Sports & Recreation