The 29-year-old struggled during his rookie year after being selected in the first round of the 2012 draft and as a result, the Browns brought in Jason Campbell and Brian Hoyer to provide competition in training camp.
Turner told the Cleveland Plain Dealer: "We're getting Brandon ready to be the starter.
"He's getting a big chunk of the work, but we're getting the other two guys ready to play.
"As we know, you better have all three of those guys ready to play in this league."
Weeden threw 14 touchdowns for the Browns in his first year in the NFL.