The Green Bay Packers have 64 players under contract as of Monday, April 3, according to Over the Cap (note: there is a discrepancy, safety Vernon Scott is listed as under contract at OTC but is not listed on the Packers current roster.)
Teams can roster 90 players during the offseason and into training camp, so the Packers will, at various points, add 27 players between now and late July.
