31-year-old Sheron's contract expired at the end of the season and he has been told that he will not be offered a new one in the summer.
Sheron has played over 170 games in his four years at the club and is the biggest name to be told he can leave, along with New Zealand youth international winger Leo Bertos and 22-year-old defender James Dudgeon - who looks set to join Conference side Scarborough.
Tykes boss Glyn Hodges is also looking to keep some senior members of his squad, and Dyer and Ward have been pencilled in for talks over a new deal this week.
Dyer has banged in 18 goals this season and is the club's current Player of the Year, while experienced Ward and Academy product Carl Barrowclough are also to talk over new deals.
Hodges is also looking to build for the future and has offered youngsters David Mulligan, Neil Austin, Rory Fallon and Griff Jones new deals, while young keeper Matthew Ghent has been handed a short-term deal.
