Barnet have transfer listed strikers Jake Hyde and Keanu Marsh-Brown.
Jamal Lowe has also been made available, while Nick Jupp, Freddie Warren, Ahmed Abdulla and Harry Crawford have all been released.
Mark Byrne and Curtis Weston are to be offered new deals but Mauro Vilhete's future is undecided, as is that of first-team coach Dick Schreuder.
Head of recruitment Omar Yabroudi is leaving along with head of youth sports science Konstantinos Lofitis.
Hyde, 23, scored 12 goals for the Bees this season - one more than former Fulham trainee Marsh-Brown.
Manager Martin Allen has told Marsh-Brown, 21, he is being offloaded for financial reasons.
Hyde, meanwhile, will be offered a new contract but has expressed a desire to move on, so the club have made him available to see if there is any interest.
"Jake has expressed a wish to play at a higher level and his goals over the past two seasons can make that happen," Allen told the club website.
"We are placing Jake on the transfer list to see if there are clubs in the Football League who will pay the necessary compensation.
"Our chat was honest and to the point and if no-one comes in for him then he will be a Barnet player next season."
Allen added: "I am undecided whether to take Mauro Vilhete on for another year.
"Omar and Kostas have both done a fantastic job but currently all available funds must go into strengthening the first team. Both men are excellent at their jobs and will be missed.
"Dick is currently in Holland having surgery on a tooth and we will be talking to Dick once he has recovered."
Barnet last week gave new deals to David Stephens, Luisma Villa and Andy Yiadom, but James Harper, Jon Nurse and Jack Saville were released.