Despite being a mainstay in the Gills' backline last season alongside Leon Legge, the summer arrivals of John Elgan and Kortney Hause have forced the 34-year-old down the pecking order at Priestfield.
Barrett has made 87 appearances for the club since joining from Bournemouth in 2012.
"This is one of the sides of the job that you don't like because there are times you have to make big decisions on players," boss Taylor told the official club website.
"But in the end I've made a decision that I didn't think he was going to start as many matches this year as he would have liked.
"We've made him available and I hope for his sake that something comes along."